89 Publications

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[89]
2019 | Journal Article | IST-REx-ID: 170   OA
T. D. Browning and E. Sofos, “Counting rational points on quartic del Pezzo surfaces with a rational conic,” Mathematische Annalen, vol. 373, no. 3–4, pp. 977–1016, 2019.
View | Files available | DOI | arXiv
 
[88]
2019 | Journal Article | IST-REx-ID: 175   OA
T. D. Browning and D. Loughran, “Sieving rational points on varieties,” Transactions of the American Mathematical Society, vol. 371, no. 8, pp. 5757–5785, 2019.
View | Download (ext.) | arXiv
 
[87]
2019 | Journal Article | IST-REx-ID: 6310   OA
T. D. Browning and L. Q. Hu, “ Counting rational points on biquadratic hypersurfaces,” Advances in Mathematics, vol. 349, pp. 920–940, 2019.
View | Files available | DOI | arXiv
 
[86]
2018 | Conference Paper | IST-REx-ID: 174
T. D. Browning, “How often does the Hasse principle hold?,” presented at the Algebraic Geometry, Salt Lake City, Utah, USA, 2018, vol. 97, no. 2, pp. 89–102.
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[85]
2018 | Preprint | IST-REx-ID: 179   OA
T. D. Browning and R. Heath Brown, “Density of rational points on a quadric bundle in ℙ3×ℙ3,” Unknown. Unknown, pp. 1–60, 2018.
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[84]
2018 | Preprint | IST-REx-ID: 176   OA
T. D. Browning and E. Sofos, “Averages of arithmetic functions over principal ideals,” International Journal of Nuber Theory. World Scientific Publishing, pp. 1–22, 2018.
View | Download (ext.) | arXiv
 
[83]
2018 | Journal Article | IST-REx-ID: 178   OA
T. D. Browning and R. Heath-Brown, “Counting rational points on quadric surfaces,” Discrete Analysis, pp. 1–31, 2018.
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[82]
2017 | Journal Article | IST-REx-ID: 268   OA
T. D. Browning and S. Prendiville, “A transference approach to a Roth-type theorem in the squares,” International Mathematics Research Notices, vol. 2017, no. 7, pp. 2219–2248, 2017.
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[81]
2017 | Journal Article | IST-REx-ID: 270   OA
T. D. Browning and A. Gorodnik, “Power-free values of polynomials on symmetric varieties,” Proceedings of the London Mathematical Society, vol. 114, no. 6, pp. 1044–1080, 2017.
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[80]
2017 | Journal Article | IST-REx-ID: 269   OA
T. D. Browning and D. Loughran, “Varieties with too many rational points,” Mathematische Zeitschrift, vol. 285, no. 3–4, pp. 1249–1267, 2017.
View | DOI | Download (ext.) | arXiv
 
[79]
2017 | Journal Article | IST-REx-ID: 271   OA
T. D. Browning and S. Prendiville, “Improvements in Birch’s theorem on forms in many variables,” Journal fur die Reine und Angewandte Mathematik, vol. 2017, no. 731, pp. 203–234, 2017.
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[78]
2017 | Journal Article | IST-REx-ID: 169   OA
T. D. Browning, V. Kumaraswamy, and R. Steiner, “Twisted Linnik implies optimal covering exponent for S3,” International Mathematics Research Notices, 2017.
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[77]
2017 | Journal Article | IST-REx-ID: 265
T. D. Browning and P. Vishe, “Rational curves on smooth hypersurfaces of low degree,” Geometric Methods in Algebra and Number Theory, vol. 11, no. 7, pp. 1657–1675, 2017.
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[76]
2017 | Journal Article | IST-REx-ID: 272   OA
T. D. Browning and L. Matthiesen, “Norm forms for arbitrary number fields as products of linear polynomials,” Annales Scientifiques de l’Ecole Normale Superieure, vol. 50, no. 6, pp. 1383–1446, 2017.
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[75]
2017 | Preprint | IST-REx-ID: 177   OA
T. D. Browning and W. Sawin, “A geometric version of the circle method,” Unknown. Unknown, pp. 1–47, 2017.
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[74]
2017 | Journal Article | IST-REx-ID: 172   OA
T. D. Browning and D. Schindler, “Strong approximation and a conjecture of Harpaz and Wittenberg,” International Mathematics Research Notices, 2017.
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[73]
2017 | Journal Article | IST-REx-ID: 266   OA
T. D. Browning and R. Heath Brown, “Forms in many variables and differing degrees,” Journal of the European Mathematical Society, vol. 19, no. 2, pp. 357–394, 2017.
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[72]
2017 | Journal Article | IST-REx-ID: 267
T. D. Browning, “Many cubic surfaces contain rational points,” Mathematika, vol. 63, no. 3, pp. 818–839, 2017.
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[71]
2016 | Journal Article | IST-REx-ID: 263   OA
R. De La Bretèche, T. D. Browning, and P. Salberger, “Counting rational points on the Cayley ruled cubic,” European Journal of Mathematics, vol. 2, no. 1, pp. 55–72, 2016.
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[70]
2016 | Journal Article | IST-REx-ID: 264   OA
M. Bright, T. D. Browning, and D. Loughran, “Failures of weak approximation in families,” Compositio Mathematica, vol. 152, no. 7, pp. 1435–1475, 2016.
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[69]
2016 | Journal Article | IST-REx-ID: 261
T. D. Browning and I. Vinogradov, “Effective ratner theorem for SL (2, R) ⋉R2 and gaps in √n modulo 1,” Journal of the London Mathematical Society, vol. 94, no. 1, pp. 61–84, 2016.
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[68]
2016 | Journal Article | IST-REx-ID: 173   OA
T. D. Browning and A. Booker, “Square-free values of reducible polynomials,” Discrete Analysis, vol. 8, pp. 1–18, 2016.
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[67]
2016 | Journal Article | IST-REx-ID: 262   OA
T. D. Browning and R. Newton, “The proportion of failures of the Hasse norm principle,” Mathematika, vol. 62, no. 2, pp. 337–347, 2016.
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[66]
2015 | Journal Article | IST-REx-ID: 256   OA
T. D. Browning and S. Prendiville, “Improvements in Birch’s theorem on forms in many variables,” Journal fur die Reine und Angewandte Mathematik, vol. 2017, no. 731, 2015.
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[65]
2015 | Journal Article | IST-REx-ID: 257   OA
T. D. Browning and R. Munshi, “Pairs of diagonal quadratic forms and linear correlations among sums of two squares,” Forum Mathematicum, vol. 27, no. 4, pp. 2025–2050, 2015.
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[64]
2015 | Journal Article | IST-REx-ID: 260
T. D. Browning, R. Dietmann, and R. Heath Brown, “Erratum Rational points on intersections of cubic and quadric hypersurfaces,” Journal of the Institute of Mathematics of Jussieu, vol. 14, no. 4, 2015.
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[63]
2015 | Book Chapter | IST-REx-ID: 258
T. D. Browning, “A survey of applications of the circle method to rational points,” in Arithmetic and Geometry, Cambridge University Press, 2015, pp. 89–113.
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[62]
2015 | Journal Article | IST-REx-ID: 259
T. D. Browning and P. Vishe, “Rational points on cubic hypersurfaces over F_q(t) ,” Geometric and Functional Analysis, vol. 25, no. 3, pp. 671–732, 2015.
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[61]
2014 | Journal Article | IST-REx-ID: 249
T. D. Browning and P. Vishe, “Cubic hypersurfaces and a version of the circle method for number fields,” Duke Mathematical Journal, vol. 163, no. 10, pp. 1825–1883, 2014.
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[60]
2014 | Journal Article | IST-REx-ID: 252
T. D. Browning and M. Jones, “Counting rational points on del Pezzo surfaces with a conic bundle structure,” Acta Arithmetica, vol. 163, no. 3, pp. 271–298, 2014.
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[59]
2014 | Journal Article | IST-REx-ID: 6319   OA
R. de la Bretèche and T. D. Browning, “Contre-exemples au principe de Hasse pour certains tores coflasques,” Journal de Théorie des Nombres de Bordeaux, vol. 26, no. 1, pp. 25–44, 2014.
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[58]
2014 | Journal Article | IST-REx-ID: 254
T. D. Browning, “The polynomial sieve and equal sums of like polynomials,” International Mathematics Research Notices, vol. 2015, no. 7, pp. 1987–2019, 2014.
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[57]
2014 | Journal Article | IST-REx-ID: 248   OA
T. D. Browning, L. Matthiesen, and A. Skorobogatov, “Rational points on pencils of conics and quadrics with many degenerate fibres,” Annals of Mathematics, vol. 180, no. 1, pp. 381–402, 2014.
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[56]
2014 | Journal Article | IST-REx-ID: 255
T. D. Browning, R. Dietmann, and R. Heath Brown, “Rational points on intersections of cubic and quadric hypersurfaces,” Journal of the Institute of Mathematics of Jussieu, vol. 14, no. 4, pp. 703–749, 2014.
View | DOI
 
[55]
2013 | Journal Article | IST-REx-ID: 251
R. De La Bretèche and T. D. Browning, “Counter examples to the Hasse principle among certain coflasque tori,” Journal de Theorie des Nombres de Bordeaux, vol. 26, no. 1, pp. 25–44, 2013.
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[54]
2013 | Journal Article | IST-REx-ID: 245   OA
S. Baier and T. D. Browning, “Inhomogeneous cubic congruences and rational points on del Pezzo surfaces,” Journal fur die Reine und Angewandte Mathematik, no. 680, pp. 69–151, 2013.
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[53]
2013 | Journal Article | IST-REx-ID: 246
T. D. Browning and R. Munshi, “Rational points on singular intersections of quadrics,” Compositio Mathematica, vol. 149, no. 9, pp. 1457–1494, 2013.
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[52]
2013 | Journal Article | IST-REx-ID: 253
T. D. Browning, “Counting rational points on cubic hypersurfaces: Corrigendum,” Mathematika, vol. 60, no. 1, pp. 101–107, 2013.
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[51]
2013 | Journal Article | IST-REx-ID: 247
T. D. Browning, “The Lang-Weil estimate for cubic hypersurfaces,” Canadian Mathematical Bulletin, vol. 56, no. 3, pp. 500–502, 2013.
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[50]
2013 | Journal Article | IST-REx-ID: 250   OA
R. De La Bretèche and T. D. Browning, “Density of Châtelet surfaces failing the Hasse principle,” Proceedings of the London Mathematical Society, vol. 108, no. 4, pp. 1030–1078, 2013.
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[49]
2012 | Journal Article | IST-REx-ID: 237
R. De La Bretèche, T. D. Browning, and E. Peyre, “On Manin’s conjecture for a family of Châtelet surfaces,” Annals of Mathematics, vol. 175, no. 1, pp. 297–343, 2012.
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[48]
2012 | Journal Article | IST-REx-ID: 244   OA
T. D. Browning and A. Haynes, “Incomplete kloosterman sums and multiplicative inverses in short intervals,” International Journal of Number Theory, vol. 9, no. 2, pp. 481–486, 2012.
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[47]
2012 | Journal Article | IST-REx-ID: 238
S. Baier and T. D. Browning, “Inhomogeneous quadratic congruences,” Functiones et Approximatio, Commentarii Mathematici, vol. 47, no. 2, pp. 267–286, 2012.
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[46]
2012 | Journal Article | IST-REx-ID: 240
T. D. Browning and K. V. Valckenborgh, “Sums of three squareful numbers,” Experimental Mathematics, vol. 21, no. 2, pp. 204–211, 2012.
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[45]
2012 | Journal Article | IST-REx-ID: 171   OA
T. D. Browning and S. Baier, “Inhomogeneous cubic congruences and rational points on del Pezzo surfaces,” Journal fur die Reine und Angewandte Mathematik, vol. 2013, no. 680, pp. 1–65, 2012.
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[44]
2012 | Journal Article | IST-REx-ID: 241
R. De La Bretèche and T. D. Browning, “Binary forms as sums of two squares and Châtelet surfaces,” Israel Journal of Mathematics, vol. 191, no. 2, pp. 973–1012, 2012.
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[43]
2012 | Journal Article | IST-REx-ID: 242   OA
S. Baier, T. D. Browning, G. Marasingha, and L. Zhao, “Averages of shifted convolutions of d3 (n),” Proceedings of the Edinburgh Mathematical Society, vol. 55, no. 3, pp. 551–576, 2012.
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[42]
2012 | Journal Article | IST-REx-ID: 243
T. D. Browning and R. Heath Brown, “Quadratic polynomials represented by norm forms,” Geometric and Functional Analysis, vol. 22, no. 5, pp. 1124–1190, 2012.
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[41]
2011 | Journal Article | IST-REx-ID: 233
T. D. Browning, “Power-free values of polynomials,” Archiv der Mathematik, vol. 96, no. 2, pp. 139–150, 2011.
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[40]
2011 | Journal Article | IST-REx-ID: 234
T. D. Browning, “The divisor problem for binary cubic forms,” Journal de Theorie des Nombres de Bordeaux, vol. 23, no. 3, pp. 579–602, 2011.
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[39]
2011 | Journal Article | IST-REx-ID: 239
T. D. Browning, R. Dietmann, and P. Elliott, “Least zero of a cubic form,” Mathematische Annalen, vol. 352, no. 3, pp. 745–778, 2011.
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[38]
2011 | Journal Article | IST-REx-ID: 235
T. D. Browning and C. Elsholtz, “The number of representations of rationals as a sum of unit fractions,” Illinois Journal of Mathematics, vol. 55, no. 2, pp. 685–696, 2011.
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[37]
2011 | Journal Article | IST-REx-ID: 236
R. De La Bretèche and T. D. Browning, “Manin’s conjecture for quartic Del Pezzo surfaces with a conic fibration,” Duke Mathematical Journal, vol. 160, no. 1, pp. 1–69, 2011.
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[36]
2010 | Journal Article | IST-REx-ID: 6320   OA
R. de la Bretèche and T. D. Browning, “Le problème des diviseurs pour des formes binaires de degré 4,” Crelles Journal, vol. 2010, no. 646, pp. 1–44, 2010.
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[35]
2010 | Journal Article | IST-REx-ID: 231
T. D. Browning and J. Colliot Thélène, “Rational points on cubic hypersurfaces that split off a form. With an appendix by J-L Colliot-Thélène,” Compositio Mathematica, vol. 146, no. 4, pp. 853–885, 2010.
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[34]
2009 | Book Chapter | IST-REx-ID: 168
T. D. Browning and R. Dietmann, “Solubility of Fermat equations,” in Quadratic Forms - algebra, arithmetic and geometry, vol. 493, American Mathematical Society, 2009, pp. 99–106.
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[33]
2009 | Journal Article | IST-REx-ID: 226
T. D. Browning and U. Derenthal, “Manin’s conjecture for a quartic del Pezzo surface with A4 singularity,” Annales de l’Institut Fourier, vol. 59, no. 3, pp. 1231–1265, 2009.
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[32]
2009 | Book Chapter | IST-REx-ID: 164   OA
T. D. Browning and R. Heath Brown, “Integral points on cubic hypersurfaces,” in Analytic Number Theory: Essays in honour of Klaus Roth, Cambridge University Press, 2009, pp. 75–90.
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[31]
2009 | Book | IST-REx-ID: 227
T. D. Browning, Quantitative arithmetic of projective varieties, vol. 277. Birkhäuser Basel, 2009, pp. 1–160.
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[30]
2009 | Conference Paper | IST-REx-ID: 165
T. D. Browning, “Resent progress on the quantitative arithmetic of del Pezzo surfaces,” presented at the Number Theory: Dreaming in dreams, 2009, vol. 6, pp. 1–18.
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[29]
2009 | Journal Article | IST-REx-ID: 230
T. D. Browning and U. Derenthal, “Manin’s conjecture for a cubic surface with  D 5 singularity,” International Mathematics Research Notices, vol. 2009, no. 14, pp. 2620–2647, 2009.
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[28]
2009 | Journal Article | IST-REx-ID: 228   OA
T. D. Browning and R. Heath Brown, “Rational points on quartic hypersurfaces,” Journal fur die Reine und Angewandte Mathematik, no. 629, pp. 37–88, 2009.
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[27]
2009 | Journal Article | IST-REx-ID: 229   OA
T. D. Browning, “Linear growth for Châtelet surfaces,” Mathematische Annalen, vol. 346, no. 1, pp. 41–50, 2009.
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[26]
2008 | Journal Article | IST-REx-ID: 225
R. De La Bretèche and T. D. Browning, “Binary linear forms as sums of two squares,” Compositio Mathematica, vol. 144, no. 6, pp. 1375–1402, 2008.
View | DOI
 
[25]
2008 | Journal Article | IST-REx-ID: 224
T. D. Browning and R. Dietmann, “On the representation of integers by quadratic forms,” Proceedings of the London Mathematical Society, vol. 96, no. 2, pp. 389–416, 2008.
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[24]
2007 | Book Chapter | IST-REx-ID: 167   OA
T. D. Browning and R. Heath Brown, “Simultaneous equal sums of three powers,” in Diophantine Geometry, vol. 4, U. Zannier, Ed. Edizioni della Normale, 2007, pp. 93–100.
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[23]
2007 | Journal Article | IST-REx-ID: 220
T. D. Browning, “Counting rational points on cubic hypersurfaces,” Mathematika, vol. 54, no. 1–2, pp. 93–112, 2007.
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[22]
2007 | Journal Article | IST-REx-ID: 219
R. De La Bretèche, T. D. Browning, and U. Derenthal, “On Manin’s conjecture for a certain singular cubic surface,” Annales Scientifiques de l’Ecole Normale Superieure, vol. 40, no. 1, pp. 1–50, 2007.
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[21]
2007 | Journal Article | IST-REx-ID: 221   OA
R. De La Bretèche and T. D. Browning, “On Manin’s conjecture for singular del Pezzo surfaces of degree four, I,” Michigan Mathematical Journal, vol. 55, no. 1, pp. 51–80, 2007.
View | Files available | DOI | arXiv
 
[20]
2007 | Preprint | IST-REx-ID: 6321   OA
T. D. Browning, “The Manin conjecture in dimension 2,” Arxiv. Arxiv, pp. 1–57, 2007.
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[19]
2007 | Journal Article | IST-REx-ID: 222   OA
R. De La Bretèche and T. D. Browning, “On Manin’s conjecture for singular del Pezzo surfaces of degree four, II,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 143, no. 3, pp. 579–605, 2007.
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[18]
2007 | Journal Article | IST-REx-ID: 223   OA
T. D. Browning, “Density of integer solutions to diagonal quadratic forms,” Monatshefte fur Mathematik, vol. 152, no. 1, pp. 13–38, 2007.
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[17]
2007 | Book Chapter | IST-REx-ID: 6323   OA
T. D. Browning, “An overview of Manin’s conjecture for del Pezzo surfaces,” in A Tribute to Gauss and Dirichlet, vol. 7, American Mathematical Society, 2007, pp. 39–56.
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[16]
2006 | Journal Article | IST-REx-ID: 213
T. D. Browning, R. Heath Brown, and J. Starr, “The density of rational points on non-singular hypersurfaces, II,” Proceedings of the London Mathematical Society, vol. 93, no. 2, pp. 273–303, 2006.
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[15]
2006 | Journal Article | IST-REx-ID: 218
R. De La Bretèche and T. D. Browning, “Sums of arithmetic functions over values of binary forms,” Acta Arithmetica, vol. 125, no. 3, pp. 291–304, 2006.
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[14]
2006 | Journal Article | IST-REx-ID: 215
T. D. Browning and R. Heath Brown, “The density of rational points on non-singular hypersurfaces, I,” Bulletin of the London Mathematical Society, vol. 38, no. 3, pp. 401–410, 2006.
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[13]
2006 | Journal Article | IST-REx-ID: 216
T. D. Browning, R. Heath Brown, and P. Salberger, “Counting rational points on algebraic varieties,” Duke Mathematical Journal, vol. 132, no. 3, pp. 545–578, 2006.
View | DOI
 
[12]
2005 | Journal Article | IST-REx-ID: 214   OA
T. D. Browning and R. Heath Brown, “Plane curves in boxes and equal sums of two powers,” Mathematische Zeitschrift, vol. 251, no. 2, pp. 233–247, 2005.
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[11]
2005 | Book | IST-REx-ID: 210
H. Davenport and T. D. Browning, Analytic methods for diophantine equations and diophantine inequalities. Cambridge University Press, 2005, pp. 1–140.
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[10]
2005 | Journal Article | IST-REx-ID: 211
T. D. Browning, “Equal sums of like polynomials,” Bulletin of the London Mathematical Society, vol. 37, no. 6, pp. 801–808, 2005.
View | DOI
 
[9]
2005 | Journal Article | IST-REx-ID: 217
T. D. Browning, “The density of rational points on a certain singular cubic surface,” Journal of Number Theory, vol. 119, no. 2, pp. 242–283, 2005.
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[8]
2005 | Journal Article | IST-REx-ID: 212   OA
T. D. Browning and R. Heath Brown, “Counting rational points on hypersurfaces,” Journal fur die Reine und Angewandte Mathematik, no. 584, pp. 83–115, 2005.
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[7]
2004 | Journal Article | IST-REx-ID: 209
T. D. Browning and R. Heath Brown, “Equal sums of three powers,” Inventiones Mathematicae, vol. 157, no. 3, pp. 553–573, 2004.
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[6]
2003 | Journal Article | IST-REx-ID: 206
T. D. Browning, “A note on the distribution of rational points on threefolds,” Quarterly Journal of Mathematics, vol. 54, no. 1, pp. 33–39, 2003.
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[5]
2003 | Journal Article | IST-REx-ID: 207
T. D. Browning, “Sums of four biquadrates,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 134, no. 3, pp. 385–395, 2003.
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[4]
2003 | Journal Article | IST-REx-ID: 208
T. D. Browning, “Counting rational points on diagonal quadratic surfaces,” Quarterly Journal of Mathematics, vol. 54, no. 1, pp. 11–31, 2003.
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[3]
2003 | Journal Article | IST-REx-ID: 166   OA
T. D. Browning and M. Swarbick Jones, “Counting rational points on del Pezzo surfaces of degree 5,” Proceedings of the Bonn session in analytic number theory and diophantine equations, vol. 360, 2003.
View | Download (ext.) | arXiv
 
[2]
2003 | Journal Article | IST-REx-ID: 205
T. D. Browning, “Counting rational points on cubic and quartic surfaces,” Acta Arithmetica, vol. 108, no. 3, pp. 275–295, 2003.
View | DOI
 
[1]
2002 | Journal Article | IST-REx-ID: 204
T. D. Browning, “Equal Sums of Two kth Powers,” Journal of Number Theory, vol. 96, no. 2, pp. 293–318, 2002.
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89 Publications

Mark all

[89]
2019 | Journal Article | IST-REx-ID: 170   OA
T. D. Browning and E. Sofos, “Counting rational points on quartic del Pezzo surfaces with a rational conic,” Mathematische Annalen, vol. 373, no. 3–4, pp. 977–1016, 2019.
View | Files available | DOI | arXiv
 
[88]
2019 | Journal Article | IST-REx-ID: 175   OA
T. D. Browning and D. Loughran, “Sieving rational points on varieties,” Transactions of the American Mathematical Society, vol. 371, no. 8, pp. 5757–5785, 2019.
View | Download (ext.) | arXiv
 
[87]
2019 | Journal Article | IST-REx-ID: 6310   OA
T. D. Browning and L. Q. Hu, “ Counting rational points on biquadratic hypersurfaces,” Advances in Mathematics, vol. 349, pp. 920–940, 2019.
View | Files available | DOI | arXiv
 
[86]
2018 | Conference Paper | IST-REx-ID: 174
T. D. Browning, “How often does the Hasse principle hold?,” presented at the Algebraic Geometry, Salt Lake City, Utah, USA, 2018, vol. 97, no. 2, pp. 89–102.
View | DOI
 
[85]
2018 | Preprint | IST-REx-ID: 179   OA
T. D. Browning and R. Heath Brown, “Density of rational points on a quadric bundle in ℙ3×ℙ3,” Unknown. Unknown, pp. 1–60, 2018.
View | Download (ext.)
 
[84]
2018 | Preprint | IST-REx-ID: 176   OA
T. D. Browning and E. Sofos, “Averages of arithmetic functions over principal ideals,” International Journal of Nuber Theory. World Scientific Publishing, pp. 1–22, 2018.
View | Download (ext.) | arXiv
 
[83]
2018 | Journal Article | IST-REx-ID: 178   OA
T. D. Browning and R. Heath-Brown, “Counting rational points on quadric surfaces,” Discrete Analysis, pp. 1–31, 2018.
View | DOI | Download (ext.) | arXiv
 
[82]
2017 | Journal Article | IST-REx-ID: 268   OA
T. D. Browning and S. Prendiville, “A transference approach to a Roth-type theorem in the squares,” International Mathematics Research Notices, vol. 2017, no. 7, pp. 2219–2248, 2017.
View | DOI | Download (ext.)
 
[81]
2017 | Journal Article | IST-REx-ID: 270   OA
T. D. Browning and A. Gorodnik, “Power-free values of polynomials on symmetric varieties,” Proceedings of the London Mathematical Society, vol. 114, no. 6, pp. 1044–1080, 2017.
View | DOI | Download (ext.)
 
[80]
2017 | Journal Article | IST-REx-ID: 269   OA
T. D. Browning and D. Loughran, “Varieties with too many rational points,” Mathematische Zeitschrift, vol. 285, no. 3–4, pp. 1249–1267, 2017.
View | DOI | Download (ext.) | arXiv
 
[79]
2017 | Journal Article | IST-REx-ID: 271   OA
T. D. Browning and S. Prendiville, “Improvements in Birch’s theorem on forms in many variables,” Journal fur die Reine und Angewandte Mathematik, vol. 2017, no. 731, pp. 203–234, 2017.
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[78]
2017 | Journal Article | IST-REx-ID: 169   OA
T. D. Browning, V. Kumaraswamy, and R. Steiner, “Twisted Linnik implies optimal covering exponent for S3,” International Mathematics Research Notices, 2017.
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[77]
2017 | Journal Article | IST-REx-ID: 265
T. D. Browning and P. Vishe, “Rational curves on smooth hypersurfaces of low degree,” Geometric Methods in Algebra and Number Theory, vol. 11, no. 7, pp. 1657–1675, 2017.
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[76]
2017 | Journal Article | IST-REx-ID: 272   OA
T. D. Browning and L. Matthiesen, “Norm forms for arbitrary number fields as products of linear polynomials,” Annales Scientifiques de l’Ecole Normale Superieure, vol. 50, no. 6, pp. 1383–1446, 2017.
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[75]
2017 | Preprint | IST-REx-ID: 177   OA
T. D. Browning and W. Sawin, “A geometric version of the circle method,” Unknown. Unknown, pp. 1–47, 2017.
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[74]
2017 | Journal Article | IST-REx-ID: 172   OA
T. D. Browning and D. Schindler, “Strong approximation and a conjecture of Harpaz and Wittenberg,” International Mathematics Research Notices, 2017.
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[73]
2017 | Journal Article | IST-REx-ID: 266   OA
T. D. Browning and R. Heath Brown, “Forms in many variables and differing degrees,” Journal of the European Mathematical Society, vol. 19, no. 2, pp. 357–394, 2017.
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[72]
2017 | Journal Article | IST-REx-ID: 267
T. D. Browning, “Many cubic surfaces contain rational points,” Mathematika, vol. 63, no. 3, pp. 818–839, 2017.
View | DOI
 
[71]
2016 | Journal Article | IST-REx-ID: 263   OA
R. De La Bretèche, T. D. Browning, and P. Salberger, “Counting rational points on the Cayley ruled cubic,” European Journal of Mathematics, vol. 2, no. 1, pp. 55–72, 2016.
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[70]
2016 | Journal Article | IST-REx-ID: 264   OA
M. Bright, T. D. Browning, and D. Loughran, “Failures of weak approximation in families,” Compositio Mathematica, vol. 152, no. 7, pp. 1435–1475, 2016.
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[69]
2016 | Journal Article | IST-REx-ID: 261
T. D. Browning and I. Vinogradov, “Effective ratner theorem for SL (2, R) ⋉R2 and gaps in √n modulo 1,” Journal of the London Mathematical Society, vol. 94, no. 1, pp. 61–84, 2016.
View | DOI
 
[68]
2016 | Journal Article | IST-REx-ID: 173   OA
T. D. Browning and A. Booker, “Square-free values of reducible polynomials,” Discrete Analysis, vol. 8, pp. 1–18, 2016.
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[67]
2016 | Journal Article | IST-REx-ID: 262   OA
T. D. Browning and R. Newton, “The proportion of failures of the Hasse norm principle,” Mathematika, vol. 62, no. 2, pp. 337–347, 2016.
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[66]
2015 | Journal Article | IST-REx-ID: 256   OA
T. D. Browning and S. Prendiville, “Improvements in Birch’s theorem on forms in many variables,” Journal fur die Reine und Angewandte Mathematik, vol. 2017, no. 731, 2015.
View | DOI | Download (ext.)
 
[65]
2015 | Journal Article | IST-REx-ID: 257   OA
T. D. Browning and R. Munshi, “Pairs of diagonal quadratic forms and linear correlations among sums of two squares,” Forum Mathematicum, vol. 27, no. 4, pp. 2025–2050, 2015.
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[64]
2015 | Journal Article | IST-REx-ID: 260
T. D. Browning, R. Dietmann, and R. Heath Brown, “Erratum Rational points on intersections of cubic and quadric hypersurfaces,” Journal of the Institute of Mathematics of Jussieu, vol. 14, no. 4, 2015.
View | DOI
 
[63]
2015 | Book Chapter | IST-REx-ID: 258
T. D. Browning, “A survey of applications of the circle method to rational points,” in Arithmetic and Geometry, Cambridge University Press, 2015, pp. 89–113.
View | DOI
 
[62]
2015 | Journal Article | IST-REx-ID: 259
T. D. Browning and P. Vishe, “Rational points on cubic hypersurfaces over F_q(t) ,” Geometric and Functional Analysis, vol. 25, no. 3, pp. 671–732, 2015.
View | DOI
 
[61]
2014 | Journal Article | IST-REx-ID: 249
T. D. Browning and P. Vishe, “Cubic hypersurfaces and a version of the circle method for number fields,” Duke Mathematical Journal, vol. 163, no. 10, pp. 1825–1883, 2014.
View | DOI
 
[60]
2014 | Journal Article | IST-REx-ID: 252
T. D. Browning and M. Jones, “Counting rational points on del Pezzo surfaces with a conic bundle structure,” Acta Arithmetica, vol. 163, no. 3, pp. 271–298, 2014.
View | DOI
 
[59]
2014 | Journal Article | IST-REx-ID: 6319   OA
R. de la Bretèche and T. D. Browning, “Contre-exemples au principe de Hasse pour certains tores coflasques,” Journal de Théorie des Nombres de Bordeaux, vol. 26, no. 1, pp. 25–44, 2014.
View | DOI | Download (ext.) | arXiv
 
[58]
2014 | Journal Article | IST-REx-ID: 254
T. D. Browning, “The polynomial sieve and equal sums of like polynomials,” International Mathematics Research Notices, vol. 2015, no. 7, pp. 1987–2019, 2014.
View | DOI
 
[57]
2014 | Journal Article | IST-REx-ID: 248   OA
T. D. Browning, L. Matthiesen, and A. Skorobogatov, “Rational points on pencils of conics and quadrics with many degenerate fibres,” Annals of Mathematics, vol. 180, no. 1, pp. 381–402, 2014.
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[56]
2014 | Journal Article | IST-REx-ID: 255
T. D. Browning, R. Dietmann, and R. Heath Brown, “Rational points on intersections of cubic and quadric hypersurfaces,” Journal of the Institute of Mathematics of Jussieu, vol. 14, no. 4, pp. 703–749, 2014.
View | DOI
 
[55]
2013 | Journal Article | IST-REx-ID: 251
R. De La Bretèche and T. D. Browning, “Counter examples to the Hasse principle among certain coflasque tori,” Journal de Theorie des Nombres de Bordeaux, vol. 26, no. 1, pp. 25–44, 2013.
View | DOI
 
[54]
2013 | Journal Article | IST-REx-ID: 245   OA
S. Baier and T. D. Browning, “Inhomogeneous cubic congruences and rational points on del Pezzo surfaces,” Journal fur die Reine und Angewandte Mathematik, no. 680, pp. 69–151, 2013.
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[53]
2013 | Journal Article | IST-REx-ID: 246
T. D. Browning and R. Munshi, “Rational points on singular intersections of quadrics,” Compositio Mathematica, vol. 149, no. 9, pp. 1457–1494, 2013.
View | DOI
 
[52]
2013 | Journal Article | IST-REx-ID: 253
T. D. Browning, “Counting rational points on cubic hypersurfaces: Corrigendum,” Mathematika, vol. 60, no. 1, pp. 101–107, 2013.
View | DOI
 
[51]
2013 | Journal Article | IST-REx-ID: 247
T. D. Browning, “The Lang-Weil estimate for cubic hypersurfaces,” Canadian Mathematical Bulletin, vol. 56, no. 3, pp. 500–502, 2013.
View | DOI
 
[50]
2013 | Journal Article | IST-REx-ID: 250   OA
R. De La Bretèche and T. D. Browning, “Density of Châtelet surfaces failing the Hasse principle,” Proceedings of the London Mathematical Society, vol. 108, no. 4, pp. 1030–1078, 2013.
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[49]
2012 | Journal Article | IST-REx-ID: 237
R. De La Bretèche, T. D. Browning, and E. Peyre, “On Manin’s conjecture for a family of Châtelet surfaces,” Annals of Mathematics, vol. 175, no. 1, pp. 297–343, 2012.
View | DOI
 
[48]
2012 | Journal Article | IST-REx-ID: 244   OA
T. D. Browning and A. Haynes, “Incomplete kloosterman sums and multiplicative inverses in short intervals,” International Journal of Number Theory, vol. 9, no. 2, pp. 481–486, 2012.
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[47]
2012 | Journal Article | IST-REx-ID: 238
S. Baier and T. D. Browning, “Inhomogeneous quadratic congruences,” Functiones et Approximatio, Commentarii Mathematici, vol. 47, no. 2, pp. 267–286, 2012.
View | DOI
 
[46]
2012 | Journal Article | IST-REx-ID: 240
T. D. Browning and K. V. Valckenborgh, “Sums of three squareful numbers,” Experimental Mathematics, vol. 21, no. 2, pp. 204–211, 2012.
View | DOI
 
[45]
2012 | Journal Article | IST-REx-ID: 171   OA
T. D. Browning and S. Baier, “Inhomogeneous cubic congruences and rational points on del Pezzo surfaces,” Journal fur die Reine und Angewandte Mathematik, vol. 2013, no. 680, pp. 1–65, 2012.
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[44]
2012 | Journal Article | IST-REx-ID: 241
R. De La Bretèche and T. D. Browning, “Binary forms as sums of two squares and Châtelet surfaces,” Israel Journal of Mathematics, vol. 191, no. 2, pp. 973–1012, 2012.
View | DOI
 
[43]
2012 | Journal Article | IST-REx-ID: 242   OA
S. Baier, T. D. Browning, G. Marasingha, and L. Zhao, “Averages of shifted convolutions of d3 (n),” Proceedings of the Edinburgh Mathematical Society, vol. 55, no. 3, pp. 551–576, 2012.
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[42]
2012 | Journal Article | IST-REx-ID: 243
T. D. Browning and R. Heath Brown, “Quadratic polynomials represented by norm forms,” Geometric and Functional Analysis, vol. 22, no. 5, pp. 1124–1190, 2012.
View | DOI
 
[41]
2011 | Journal Article | IST-REx-ID: 233
T. D. Browning, “Power-free values of polynomials,” Archiv der Mathematik, vol. 96, no. 2, pp. 139–150, 2011.
View | DOI
 
[40]
2011 | Journal Article | IST-REx-ID: 234
T. D. Browning, “The divisor problem for binary cubic forms,” Journal de Theorie des Nombres de Bordeaux, vol. 23, no. 3, pp. 579–602, 2011.
View | DOI
 
[39]
2011 | Journal Article | IST-REx-ID: 239
T. D. Browning, R. Dietmann, and P. Elliott, “Least zero of a cubic form,” Mathematische Annalen, vol. 352, no. 3, pp. 745–778, 2011.
View | DOI
 
[38]
2011 | Journal Article | IST-REx-ID: 235
T. D. Browning and C. Elsholtz, “The number of representations of rationals as a sum of unit fractions,” Illinois Journal of Mathematics, vol. 55, no. 2, pp. 685–696, 2011.
View
 
[37]
2011 | Journal Article | IST-REx-ID: 236
R. De La Bretèche and T. D. Browning, “Manin’s conjecture for quartic Del Pezzo surfaces with a conic fibration,” Duke Mathematical Journal, vol. 160, no. 1, pp. 1–69, 2011.
View | DOI
 
[36]
2010 | Journal Article | IST-REx-ID: 6320   OA
R. de la Bretèche and T. D. Browning, “Le problème des diviseurs pour des formes binaires de degré 4,” Crelles Journal, vol. 2010, no. 646, pp. 1–44, 2010.
View | DOI | Download (ext.) | arXiv
 
[35]
2010 | Journal Article | IST-REx-ID: 231
T. D. Browning and J. Colliot Thélène, “Rational points on cubic hypersurfaces that split off a form. With an appendix by J-L Colliot-Thélène,” Compositio Mathematica, vol. 146, no. 4, pp. 853–885, 2010.
View | DOI
 
[34]
2009 | Book Chapter | IST-REx-ID: 168
T. D. Browning and R. Dietmann, “Solubility of Fermat equations,” in Quadratic Forms - algebra, arithmetic and geometry, vol. 493, American Mathematical Society, 2009, pp. 99–106.
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[33]
2009 | Journal Article | IST-REx-ID: 226
T. D. Browning and U. Derenthal, “Manin’s conjecture for a quartic del Pezzo surface with A4 singularity,” Annales de l’Institut Fourier, vol. 59, no. 3, pp. 1231–1265, 2009.
View | DOI
 
[32]
2009 | Book Chapter | IST-REx-ID: 164   OA
T. D. Browning and R. Heath Brown, “Integral points on cubic hypersurfaces,” in Analytic Number Theory: Essays in honour of Klaus Roth, Cambridge University Press, 2009, pp. 75–90.
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[31]
2009 | Book | IST-REx-ID: 227
T. D. Browning, Quantitative arithmetic of projective varieties, vol. 277. Birkhäuser Basel, 2009, pp. 1–160.
View | DOI
 
[30]
2009 | Conference Paper | IST-REx-ID: 165
T. D. Browning, “Resent progress on the quantitative arithmetic of del Pezzo surfaces,” presented at the Number Theory: Dreaming in dreams, 2009, vol. 6, pp. 1–18.
View | DOI
 
[29]
2009 | Journal Article | IST-REx-ID: 230
T. D. Browning and U. Derenthal, “Manin’s conjecture for a cubic surface with  D 5 singularity,” International Mathematics Research Notices, vol. 2009, no. 14, pp. 2620–2647, 2009.
View | DOI
 
[28]
2009 | Journal Article | IST-REx-ID: 228   OA
T. D. Browning and R. Heath Brown, “Rational points on quartic hypersurfaces,” Journal fur die Reine und Angewandte Mathematik, no. 629, pp. 37–88, 2009.
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[27]
2009 | Journal Article | IST-REx-ID: 229   OA
T. D. Browning, “Linear growth for Châtelet surfaces,” Mathematische Annalen, vol. 346, no. 1, pp. 41–50, 2009.
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[26]
2008 | Journal Article | IST-REx-ID: 225
R. De La Bretèche and T. D. Browning, “Binary linear forms as sums of two squares,” Compositio Mathematica, vol. 144, no. 6, pp. 1375–1402, 2008.
View | DOI
 
[25]
2008 | Journal Article | IST-REx-ID: 224
T. D. Browning and R. Dietmann, “On the representation of integers by quadratic forms,” Proceedings of the London Mathematical Society, vol. 96, no. 2, pp. 389–416, 2008.
View | DOI
 
[24]
2007 | Book Chapter | IST-REx-ID: 167   OA
T. D. Browning and R. Heath Brown, “Simultaneous equal sums of three powers,” in Diophantine Geometry, vol. 4, U. Zannier, Ed. Edizioni della Normale, 2007, pp. 93–100.
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[23]
2007 | Journal Article | IST-REx-ID: 220
T. D. Browning, “Counting rational points on cubic hypersurfaces,” Mathematika, vol. 54, no. 1–2, pp. 93–112, 2007.
View | DOI
 
[22]
2007 | Journal Article | IST-REx-ID: 219
R. De La Bretèche, T. D. Browning, and U. Derenthal, “On Manin’s conjecture for a certain singular cubic surface,” Annales Scientifiques de l’Ecole Normale Superieure, vol. 40, no. 1, pp. 1–50, 2007.
View | DOI
 
[21]
2007 | Journal Article | IST-REx-ID: 221   OA
R. De La Bretèche and T. D. Browning, “On Manin’s conjecture for singular del Pezzo surfaces of degree four, I,” Michigan Mathematical Journal, vol. 55, no. 1, pp. 51–80, 2007.
View | Files available | DOI | arXiv
 
[20]
2007 | Preprint | IST-REx-ID: 6321   OA
T. D. Browning, “The Manin conjecture in dimension 2,” Arxiv. Arxiv, pp. 1–57, 2007.
View | Download (ext.) | arXiv
 
[19]
2007 | Journal Article | IST-REx-ID: 222   OA
R. De La Bretèche and T. D. Browning, “On Manin’s conjecture for singular del Pezzo surfaces of degree four, II,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 143, no. 3, pp. 579–605, 2007.
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[18]
2007 | Journal Article | IST-REx-ID: 223   OA
T. D. Browning, “Density of integer solutions to diagonal quadratic forms,” Monatshefte fur Mathematik, vol. 152, no. 1, pp. 13–38, 2007.
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[17]
2007 | Book Chapter | IST-REx-ID: 6323   OA
T. D. Browning, “An overview of Manin’s conjecture for del Pezzo surfaces,” in A Tribute to Gauss and Dirichlet, vol. 7, American Mathematical Society, 2007, pp. 39–56.
View | Download (ext.) | arXiv
 
[16]
2006 | Journal Article | IST-REx-ID: 213
T. D. Browning, R. Heath Brown, and J. Starr, “The density of rational points on non-singular hypersurfaces, II,” Proceedings of the London Mathematical Society, vol. 93, no. 2, pp. 273–303, 2006.
View | DOI
 
[15]
2006 | Journal Article | IST-REx-ID: 218
R. De La Bretèche and T. D. Browning, “Sums of arithmetic functions over values of binary forms,” Acta Arithmetica, vol. 125, no. 3, pp. 291–304, 2006.
View | DOI
 
[14]
2006 | Journal Article | IST-REx-ID: 215
T. D. Browning and R. Heath Brown, “The density of rational points on non-singular hypersurfaces, I,” Bulletin of the London Mathematical Society, vol. 38, no. 3, pp. 401–410, 2006.
View | DOI
 
[13]
2006 | Journal Article | IST-REx-ID: 216
T. D. Browning, R. Heath Brown, and P. Salberger, “Counting rational points on algebraic varieties,” Duke Mathematical Journal, vol. 132, no. 3, pp. 545–578, 2006.
View | DOI
 
[12]
2005 | Journal Article | IST-REx-ID: 214   OA
T. D. Browning and R. Heath Brown, “Plane curves in boxes and equal sums of two powers,” Mathematische Zeitschrift, vol. 251, no. 2, pp. 233–247, 2005.
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[11]
2005 | Book | IST-REx-ID: 210
H. Davenport and T. D. Browning, Analytic methods for diophantine equations and diophantine inequalities. Cambridge University Press, 2005, pp. 1–140.
View | DOI
 
[10]
2005 | Journal Article | IST-REx-ID: 211
T. D. Browning, “Equal sums of like polynomials,” Bulletin of the London Mathematical Society, vol. 37, no. 6, pp. 801–808, 2005.
View | DOI
 
[9]
2005 | Journal Article | IST-REx-ID: 217
T. D. Browning, “The density of rational points on a certain singular cubic surface,” Journal of Number Theory, vol. 119, no. 2, pp. 242–283, 2005.
View | DOI
 
[8]
2005 | Journal Article | IST-REx-ID: 212   OA
T. D. Browning and R. Heath Brown, “Counting rational points on hypersurfaces,” Journal fur die Reine und Angewandte Mathematik, no. 584, pp. 83–115, 2005.
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[7]
2004 | Journal Article | IST-REx-ID: 209
T. D. Browning and R. Heath Brown, “Equal sums of three powers,” Inventiones Mathematicae, vol. 157, no. 3, pp. 553–573, 2004.
View | DOI
 
[6]
2003 | Journal Article | IST-REx-ID: 206
T. D. Browning, “A note on the distribution of rational points on threefolds,” Quarterly Journal of Mathematics, vol. 54, no. 1, pp. 33–39, 2003.
View | DOI
 
[5]
2003 | Journal Article | IST-REx-ID: 207
T. D. Browning, “Sums of four biquadrates,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 134, no. 3, pp. 385–395, 2003.
View | DOI
 
[4]
2003 | Journal Article | IST-REx-ID: 208
T. D. Browning, “Counting rational points on diagonal quadratic surfaces,” Quarterly Journal of Mathematics, vol. 54, no. 1, pp. 11–31, 2003.
View | DOI
 
[3]
2003 | Journal Article | IST-REx-ID: 166   OA
T. D. Browning and M. Swarbick Jones, “Counting rational points on del Pezzo surfaces of degree 5,” Proceedings of the Bonn session in analytic number theory and diophantine equations, vol. 360, 2003.
View | Download (ext.) | arXiv
 
[2]
2003 | Journal Article | IST-REx-ID: 205
T. D. Browning, “Counting rational points on cubic and quartic surfaces,” Acta Arithmetica, vol. 108, no. 3, pp. 275–295, 2003.
View | DOI
 
[1]
2002 | Journal Article | IST-REx-ID: 204
T. D. Browning, “Equal Sums of Two kth Powers,” Journal of Number Theory, vol. 96, no. 2, pp. 293–318, 2002.
View | DOI
 

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