[{"abstract":[{"text":"For any integers d,n ≥2, let X ⊂ Pn be a non‐singular hypersurface of degree d that is defined over the rational numbers. The main result in this paper is a proof that the number of rational points on X which have height at most B is O(Bn − 1 + ɛ), for any ɛ > 0. The implied constant in this estimate depends at most upon d, ɛ and n. 2000 Mathematics Subject Classification 11D45 (primary), 11G35, 14G05 (secondary).","lang":"eng"}],"publication":"Proceedings of the London Mathematical Society","page":"273 - 303","publist_id":"7698","publication_status":"published","date_published":"2006-09-01T00:00:00Z","date_created":"2018-12-11T11:45:14Z","date_updated":"2019-04-26T07:22:08Z","doi":"https://doi.org/10.1112/S0024611506015784","issue":"2","_id":"213","author":[{"first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Timothy Browning","last_name":"Browning"},{"last_name":"Heath Brown","full_name":"Heath-Brown, Roger","first_name":"Roger"},{"first_name":"Jason","full_name":"Starr, Jason M","last_name":"Starr"}],"day":"01","month":"09","title":"The density of rational points on non-singular hypersurfaces, II","year":"2006","quality_controlled":0,"publisher":"John Wiley and Sons Ltd","type":"journal_article","citation":{"ista":"Browning TD, Heath Brown R, Starr J. 2006. The density of rational points on non-singular hypersurfaces, II. Proceedings of the London Mathematical Society. 93(2), 273–303.","apa":"Browning, T. D., Heath Brown, R., & Starr, J. (2006). The density of rational points on non-singular hypersurfaces, II. *Proceedings of the London Mathematical Society*, *93*(2), 273–303. https://doi.org/10.1112/S0024611506015784","ieee":"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.","mla":"Browning, Timothy D., et al. “The Density of Rational Points on Non-Singular Hypersurfaces, II.” *Proceedings of the London Mathematical Society*, vol. 93, no. 2, John Wiley and Sons Ltd, 2006, pp. 273–303, doi:https://doi.org/10.1112/S0024611506015784.","ama":"Browning TD, Heath Brown R, Starr J. The density of rational points on non-singular hypersurfaces, II. *Proceedings of the London Mathematical Society*. 2006;93(2):273-303. doi:https://doi.org/10.1112/S0024611506015784","chicago":"Browning, Timothy D, Roger Heath Brown, and Jason Starr. “The Density of Rational Points on Non-Singular Hypersurfaces, II.” *Proceedings of the London Mathematical Society* 93, no. 2 (2006): 273–303. https://doi.org/10.1112/S0024611506015784.","short":"T.D. Browning, R. Heath Brown, J. Starr, Proceedings of the London Mathematical Society 93 (2006) 273–303."},"extern":1,"intvolume":" 93","volume":93,"acknowledgement":"EPSRC grant number GR/R93155/01","status":"public"},{"status":"public","acknowledgement":"This work has been supported by the Deutsche Forschungsgemeinschaft (DFG) and by the Bundesministerium für Bildung und Forschung (BMBF) (Förderkennzeichen 05 ES3XBA/5 and IB/DLR RUS 02/037). The cooperation between the groups at the universities of Kaiserslautern and Rostov-on-Don was supported by the Alexander-von-Humboldt Foundation within the framework of an institute partnership with funds from BMBF","volume":39,"intvolume":" 39","extern":1,"citation":{"mla":"Ehresmann, Arno, et al. “Predissociation of the N+2(C 2Σ+u) State Observed via C 2Σ+u → X 2Σ+g Fluorescence after Resonant 1s−1π* Excitation of N2 Molecule.” *Journal of Physics B: Atomic, Molecular and Optical Physics*, vol. 39, no. 6, IOP Publishing Ltd., 2006, pp. L119–26, doi:10.1088/0953-4075/39/6/L03.","ama":"Ehresmann A, Werner L, Klumpp S, et al. Predissociation of the N+2(C 2Σ+u) state observed via C 2Σ+u → X 2Σ+g fluorescence after resonant 1s−1π* excitation of N2 molecule. *Journal of Physics B: Atomic, Molecular and Optical Physics*. 2006;39(6):L119-L126. doi:10.1088/0953-4075/39/6/L03","chicago":"Ehresmann, Arno, Lutz Werner, Stefan Klumpp, Ph Demekhin, Mikhail Lemeshko, V. Sukhorukov, Karl Schartner, and Hans Schmoranzer. “Predissociation of the N+2(C 2Σ+u) State Observed via C 2Σ+u → X 2Σ+g Fluorescence after Resonant 1s−1π* Excitation of N2 Molecule.” *Journal of Physics B: Atomic, Molecular and Optical Physics* 39, no. 6 (2006): L119–26. https://doi.org/10.1088/0953-4075/39/6/L03.","short":"A. Ehresmann, L. Werner, S. Klumpp, P. Demekhin, M. Lemeshko, V. Sukhorukov, K. Schartner, H. Schmoranzer, Journal of Physics B: Atomic, Molecular and Optical Physics 39 (2006) L119–L126.","apa":"Ehresmann, A., Werner, L., Klumpp, S., Demekhin, P., Lemeshko, M., Sukhorukov, V., … Schmoranzer, H. (2006). Predissociation of the N+2(C 2Σ+u) state observed via C 2Σ+u → X 2Σ+g fluorescence after resonant 1s−1π* excitation of N2 molecule. *Journal of Physics B: Atomic, Molecular and Optical Physics*, *39*(6), L119–L126. https://doi.org/10.1088/0953-4075/39/6/L03","ista":"Ehresmann A, Werner L, Klumpp S, Demekhin P, Lemeshko M, Sukhorukov V, Schartner K, Schmoranzer H. 2006. Predissociation of the N+2(C 2Σ+u) state observed via C 2Σ+u → X 2Σ+g fluorescence after resonant 1s−1π* excitation of N2 molecule. Journal of Physics B: Atomic, Molecular and Optical Physics. 39(6), L119–L126.","ieee":"A. Ehresmann *et al.*, “Predissociation of the N+2(C 2Σ+u) state observed via C 2Σ+u → X 2Σ+g fluorescence after resonant 1s−1π* excitation of N2 molecule,” *Journal of Physics B: Atomic, Molecular and Optical Physics*, vol. 39, no. 6, pp. L119–L126, 2006."},"type":"journal_article","publisher":"IOP Publishing Ltd.","quality_controlled":0,"year":"2006","title":"Predissociation of the N+2(C 2Σ+u) state observed via C 2Σ+u → X 2Σ+g fluorescence after resonant 1s−1π* excitation of N2 molecule","month":"03","author":[{"full_name":"Ehresmann, Arno","first_name":"Arno","last_name":"Ehresmann"},{"first_name":"Lutz","full_name":"Werner, Lutz","last_name":"Werner"},{"first_name":"Stefan","full_name":"Klumpp, Stefan","last_name":"Klumpp"},{"last_name":"Demekhin","first_name":"Ph","full_name":"Demekhin, Ph V"},{"last_name":"Lemeshko","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","full_name":"Mikhail Lemeshko","first_name":"Mikhail","orcid":"0000-0002-6990-7802"},{"last_name":"Sukhorukov","full_name":"Sukhorukov, V. L","first_name":"V."},{"last_name":"Schartner","first_name":"Karl","full_name":"Schartner, Karl H"},{"last_name":"Schmoranzer","full_name":"Schmoranzer, Hans P","first_name":"Hans"}],"_id":"2134","day":"28","issue":"6","doi":"10.1088/0953-4075/39/6/L03","date_created":"2018-12-11T11:55:54Z","date_updated":"2020-07-14T12:45:29Z","date_published":"2006-03-28T00:00:00Z","publication_status":"published","publist_id":"4900","page":"L119 - L126","publication":"Journal of Physics B: Atomic, Molecular and Optical Physics","abstract":[{"text":"Predissociation of the N+2 C 2Σ+u(v') vibrational levels with v' ≥ 3 was observed via dispersed C 2Σ+u → X 2Σ+g fluorescence in the spectral range of 165–208 nm after resonant 1s−1π*(vr) excitation of N2 and its subsequent autoionization into the N+2 C state. This range is dominated by lines in atomic nitrogen, by overlapped C 2Σ+u(v') → X 2Σ+g(v'') vibrational band sequences with Δv = const and broad unresolved band systems (D, (2))2Πg(v') → A2Πu(v'') in the N+2 molecular ion. With very high fluorescence resolution of about 0.1 nm FWHM individual C 2Σ+u(v') → X 2Σ+g(v'') vibrational bands have been resolved. Calculation of the observed fluorescence spectra by taking into account predissociation and molecular rotation describes well the shape of both individual vibrational bands C 2Σ+u(v') → X 2Σ+g(v'') and the whole band system.","lang":"eng"}]},{"publication":"Journal of Physics B: Atomic, Molecular and Optical Physics","publist_id":"4882","page":"283 - 304","abstract":[{"text":"Fluorescence from fragments formed after the de-excitation of the N*2(1s−1π*) resonance has been measured in the spectral range of 135–190 nm. This range is dominated by lines in atomic nitrogen and lines formed by overlapping C2Σ+u(v') → X2Σ+g(v'') bands with Δv = const in the N+2 molecular ion which result from the spectator Auger decays of the N*2(1s−1π*(vr)) resonances. Ab initio calculations of the corresponding potential curves and transition probabilities showed that the observed irregular intensity dependence of the C2Σ+u(v') → X2Σ+g(v'')(Δv = const) fluorescence lines on the vibrational quantum number vr is due to transitions between vibrational levels during the reaction N2(v0 = 0)→ N*2(1s−1π*(vr)) Longrightarrow C2Σ+u(v') → X2Σ+g(v'').","lang":"eng"}],"publication_status":"published","date_created":"2018-12-11T11:55:57Z","date_updated":"2020-07-14T12:45:29Z","date_published":"2006-01-28T00:00:00Z","month":"01","title":"Studying the N+2(C2Σ+u → X2Σ+g) fluorescence excited via the 1s−1π* resonance","year":"2006","issue":"2","doi":"10.1088/0953-4075/39/2/006","_id":"2142","author":[{"first_name":"Arno","full_name":"Ehresmann, Arno","last_name":"Ehresmann"},{"first_name":"Lutz","full_name":"Werner, Lutz","last_name":"Werner"},{"last_name":"Klumpp","full_name":"Klumpp, Stefan","first_name":"Stefan"},{"last_name":"Lucht","full_name":"Lucht, S","first_name":"S"},{"first_name":"Hans","full_name":"Schmoranzer, Hans P","last_name":"Schmoranzer"},{"last_name":"Mickat","full_name":"Mickat, Sascha","first_name":"Sascha"},{"last_name":"Schill","full_name":"Schill, Rüdiger H","first_name":"Rüdiger"},{"last_name":"Schartner","first_name":"Karl","full_name":"Schartner, Karl H"},{"last_name":"Demekhin","full_name":"Demekhin, Philipp","first_name":"Philipp"},{"last_name":"Lemeshko","first_name":"Mikhail","orcid":"0000-0002-6990-7802","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","full_name":"Mikhail Lemeshko"},{"first_name":"Victor","full_name":"Sukhorukov, Victor L","last_name":"Sukhorukov"}],"day":"28","quality_controlled":0,"type":"journal_article","citation":{"chicago":"Ehresmann, Arno, Lutz Werner, Stefan Klumpp, S Lucht, Hans Schmoranzer, Sascha Mickat, Rüdiger Schill, et al. “Studying the N+2(C2Σ+u → X2Σ+g) Fluorescence Excited via the 1s−1π* Resonance.” *Journal of Physics B: Atomic, Molecular and Optical Physics* 39, no. 2 (2006): 283–304. https://doi.org/10.1088/0953-4075/39/2/006.","ama":"Ehresmann A, Werner L, Klumpp S, et al. Studying the N+2(C2Σ+u → X2Σ+g) fluorescence excited via the 1s−1π* resonance. *Journal of Physics B: Atomic, Molecular and Optical Physics*. 2006;39(2):283-304. doi:10.1088/0953-4075/39/2/006","mla":"Ehresmann, Arno, et al. “Studying the N+2(C2Σ+u → X2Σ+g) Fluorescence Excited via the 1s−1π* Resonance.” *Journal of Physics B: Atomic, Molecular and Optical Physics*, vol. 39, no. 2, IOP Publishing Ltd., 2006, pp. 283–304, doi:10.1088/0953-4075/39/2/006.","short":"A. Ehresmann, L. Werner, S. Klumpp, S. Lucht, H. Schmoranzer, S. Mickat, R. Schill, K. Schartner, P. Demekhin, M. Lemeshko, V. Sukhorukov, Journal of Physics B: Atomic, Molecular and Optical Physics 39 (2006) 283–304.","ista":"Ehresmann A, Werner L, Klumpp S, Lucht S, Schmoranzer H, Mickat S, Schill R, Schartner K, Demekhin P, Lemeshko M, Sukhorukov V. 2006. Studying the N+2(C2Σ+u → X2Σ+g) fluorescence excited via the 1s−1π* resonance. Journal of Physics B: Atomic, Molecular and Optical Physics. 39(2), 283–304.","apa":"Ehresmann, A., Werner, L., Klumpp, S., Lucht, S., Schmoranzer, H., Mickat, S., … Sukhorukov, V. (2006). Studying the N+2(C2Σ+u → X2Σ+g) fluorescence excited via the 1s−1π* resonance. *Journal of Physics B: Atomic, Molecular and Optical Physics*, *39*(2), 283–304. https://doi.org/10.1088/0953-4075/39/2/006","ieee":"A. Ehresmann *et al.*, “Studying the N+2(C2Σ+u → X2Σ+g) fluorescence excited via the 1s−1π* resonance,” *Journal of Physics B: Atomic, Molecular and Optical Physics*, vol. 39, no. 2, pp. 283–304, 2006."},"publisher":"IOP Publishing Ltd.","extern":1,"intvolume":" 39","volume":39,"status":"public"},{"status":"public","extern":1,"volume":73,"intvolume":" 73","acknowledgement":"The studies were supported by the Russian Ministry of Science and Education Grant No. R662. E.N. acknowledges partial support from the French Government *CNOUS.","publisher":"American Physical Society","type":"journal_article","citation":{"ista":"Vedrinskiǐ R, Nazarenko E, Lemeshko M, Nassif V, Proux O, Novakovich A, Joly Y. 2006. Temperature dependent XAFS studies of local atomic structure of the perovskite-type zirconates. Physical Review B - Condensed Matter and Materials Physics. 73(13).","apa":"Vedrinskiǐ, R., Nazarenko, E., Lemeshko, M., Nassif, V., Proux, O., Novakovich, A., & Joly, Y. (2006). Temperature dependent XAFS studies of local atomic structure of the perovskite-type zirconates. *Physical Review B - Condensed Matter and Materials Physics*, *73*(13). https://doi.org/10.1103/PhysRevB.73.134109","ieee":"R. Vedrinskiǐ *et al.*, “Temperature dependent XAFS studies of local atomic structure of the perovskite-type zirconates,” *Physical Review B - Condensed Matter and Materials Physics*, vol. 73, no. 13, 2006.","mla":"Vedrinskiǐ, Rostislav, et al. “Temperature Dependent XAFS Studies of Local Atomic Structure of the Perovskite-Type Zirconates.” *Physical Review B - Condensed Matter and Materials Physics*, vol. 73, no. 13, American Physical Society, 2006, doi:10.1103/PhysRevB.73.134109.","ama":"Vedrinskiǐ R, Nazarenko E, Lemeshko M, et al. Temperature dependent XAFS studies of local atomic structure of the perovskite-type zirconates. *Physical Review B - Condensed Matter and Materials Physics*. 2006;73(13). doi:10.1103/PhysRevB.73.134109","chicago":"Vedrinskiǐ, Rostislav, Elena Nazarenko, Mikhail Lemeshko, Vivian Nassif, Olivier Proux, Alexander Novakovich, and Yves Joly. “Temperature Dependent XAFS Studies of Local Atomic Structure of the Perovskite-Type Zirconates.” *Physical Review B - Condensed Matter and Materials Physics* 73, no. 13 (2006). https://doi.org/10.1103/PhysRevB.73.134109.","short":"R. Vedrinskiǐ, E. Nazarenko, M. Lemeshko, V. Nassif, O. Proux, A. Novakovich, Y. Joly, Physical Review B - Condensed Matter and Materials Physics 73 (2006)."},"quality_controlled":0,"issue":"13","doi":"10.1103/PhysRevB.73.134109","day":"17","_id":"2144","author":[{"first_name":"Rostislav","full_name":"Vedrinskiǐ, Rostislav V","last_name":"Vedrinskiǐ"},{"last_name":"Nazarenko","full_name":"Nazarenko, Elena S","first_name":"Elena"},{"last_name":"Lemeshko","full_name":"Mikhail Lemeshko","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6990-7802","first_name":"Mikhail"},{"first_name":"Vivian","full_name":"Nassif, Vivian M","last_name":"Nassif"},{"last_name":"Proux","first_name":"Olivier","full_name":"Proux, Olivier"},{"last_name":"Novakovich","full_name":"Novakovich, Alexander A","first_name":"Alexander"},{"full_name":"Joly, Yves","first_name":"Yves","last_name":"Joly"}],"title":"Temperature dependent XAFS studies of local atomic structure of the perovskite-type zirconates","month":"04","year":"2006","date_published":"2006-04-17T00:00:00Z","date_created":"2018-12-11T11:55:58Z","date_updated":"2020-07-14T12:45:29Z","publication_status":"published","abstract":[{"lang":"eng","text":"Temperature dependent preedge and extended x-ray absorption fine structure measurements at the Zr K edge for the perovskite-type zirconates Pb Zr0.515 Ti0.485 O3 (PZT), PbZr O3 (PZ), and BaZr O3 are performed. To carry out a more accurate study of the weak reconstruction of the local atomic structure we employed a combination of two techniques: (i) analysis of the preedge fine structure, and (ii) analysis of the Fourier transform of the difference between χ (k) functions obtained at different temperatures. A detailed investigation of local atomic structure in the cubic phase for all the crystals is also performed. It is shown that neither the displacive nor the order-disorder model can describe correctly the changes of local atomic structure during phase transitions in PZ and PZT. A spherical model describing the local atomic structure of perovskite-type crystals suffering structural phase transitions is proposed."}],"publication":"Physical Review B - Condensed Matter and Materials Physics","publist_id":"4881"},{"abstract":[{"text":"For any n≥3, let F ∈ Z[X0,...,Xn ] be a form of degree d *≥5 that defines a non-singular hypersurface X ⊂ Pn . The main result in this paper is a proof of the fact that the number N (F ; B) of Q-rational points on X which have height at most B satisfiesN (F ; B) = Od,ε,n (Bn −1+ε ), for any ε > 0. The implied constant in this estimate depends at most upon d, ε and n. New estimates are also obtained for the number of representations of a positive integer as the sum of three dth powers, and for the paucity of integer solutions to equal sums of like polynomials.*","lang":"eng"}],"publication":"Bulletin of the London Mathematical Society","publist_id":"7697","page":"401 - 410","publication_status":"published","date_published":"2006-12-23T00:00:00Z","date_created":"2018-12-11T11:45:15Z","date_updated":"2019-04-26T07:22:09Z","issue":"3","doi":"10.1112/S0024609305018412","day":"23","_id":"215","author":[{"last_name":"Browning","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Timothy Browning"},{"last_name":"Heath Brown","full_name":"Heath-Brown, Roger","first_name":"Roger"}],"month":"12","title":"The density of rational points on non-singular hypersurfaces, I","year":"2006","quality_controlled":0,"publisher":"Wiley-Blackwell","type":"journal_article","citation":{"ama":"Browning TD, Heath Brown R. The density of rational points on non-singular hypersurfaces, I. *Bulletin of the London Mathematical Society*. 2006;38(3):401-410. doi:10.1112/S0024609305018412","chicago":"Browning, Timothy D, and Roger Heath Brown. “The Density of Rational Points on Non-Singular Hypersurfaces, I.” *Bulletin of the London Mathematical Society* 38, no. 3 (2006): 401–10. https://doi.org/10.1112/S0024609305018412.","mla":"Browning, Timothy D., and Roger Heath Brown. “The Density of Rational Points on Non-Singular Hypersurfaces, I.” *Bulletin of the London Mathematical Society*, vol. 38, no. 3, Wiley-Blackwell, 2006, pp. 401–10, doi:10.1112/S0024609305018412.","short":"T.D. Browning, R. Heath Brown, Bulletin of the London Mathematical Society 38 (2006) 401–410.","ista":"Browning TD, Heath Brown R. 2006. The density of rational points on non-singular hypersurfaces, I. Bulletin of the London Mathematical Society. 38(3), 401–410.","apa":"Browning, T. D., & Heath Brown, R. (2006). The density of rational points on non-singular hypersurfaces, I. *Bulletin of the London Mathematical Society*, *38*(3), 401–410. https://doi.org/10.1112/S0024609305018412","ieee":"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."},"extern":1,"intvolume":" 38","volume":38,"status":"public"}]