[{"publisher":"Princeton University Press","day":"01","volume":175,"date_updated":"2021-01-12T06:57:04Z","_id":"237","extern":1,"page":"297 - 343","abstract":[{"lang":"eng","text":"The Manin conjecture is established for Châtelet surfaces over Q aris-ing as minimal proper smooth models of the surface Y 2 + Z 2 = f(X) in A 3 Q, where f ∈ Z[X] is a totally reducible polynomial of degree 3 without repeated roots. These surfaces do not satisfy weak approximation."}],"publication_status":"published","type":"journal_article","publist_id":"7667","doi":"10.4007/annals.2012.175.1.8","date_published":"2012-01-01T00:00:00Z","date_created":"2018-12-11T11:45:22Z","month":"01","issue":"1","citation":{"ista":"De La Bretèche R, Browning TD, Peyre E. 2012. On Manin’s conjecture for a family of Châtelet surfaces. Annals of Mathematics. 175(1), 297–343.","ama":"De La Bretèche R, Browning TD, Peyre E. On Manin’s conjecture for a family of Châtelet surfaces. *Annals of Mathematics*. 2012;175(1):297-343. doi:10.4007/annals.2012.175.1.8","apa":"De La Bretèche, R., Browning, T. D., & Peyre, E. (2012). On Manin’s conjecture for a family of Châtelet surfaces. *Annals of Mathematics*. Princeton University Press. https://doi.org/10.4007/annals.2012.175.1.8","mla":"De La Bretèche, Régis, et al. “On Manin’s Conjecture for a Family of Châtelet Surfaces.” *Annals of Mathematics*, vol. 175, no. 1, Princeton University Press, 2012, pp. 297–343, doi:10.4007/annals.2012.175.1.8.","chicago":"De La Bretèche, Régis, Timothy D Browning, and Emmanuel Peyre. “On Manin’s Conjecture for a Family of Châtelet Surfaces.” *Annals of Mathematics*. Princeton University Press, 2012. https://doi.org/10.4007/annals.2012.175.1.8.","ieee":"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. Princeton University Press, pp. 297–343, 2012.","short":"R. De La Bretèche, T.D. Browning, E. Peyre, Annals of Mathematics 175 (2012) 297–343."},"status":"public","author":[{"first_name":"Régis","last_name":"De La Bretèche","full_name":"de la Bretèche, Régis"},{"last_name":"Browning","first_name":"Timothy D","orcid":"0000-0002-8314-0177","full_name":"Timothy Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Emmanuel","last_name":"Peyre","full_name":"Peyre, Emmanuel"}],"intvolume":" 175","publication":"Annals of Mathematics","year":"2012","quality_controlled":0,"acknowledgement":"EP/E053262/1\tEngineering and Physical Sciences Research Council","title":"On Manin's conjecture for a family of Châtelet surfaces"},{"author":[{"last_name":"Baier","first_name":"Stephan","full_name":"Baier, Stephan"},{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Timothy Browning","last_name":"Browning","first_name":"Timothy D"}],"citation":{"chicago":"Baier, Stephan, and Timothy D Browning. “Inhomogeneous Quadratic Congruences.” *Functiones et Approximatio, Commentarii Mathematici*. Adam Mickiewicz University Press, 2012. https://doi.org/10.7169/facm/2012.47.2.9.","ieee":"S. Baier and T. D. Browning, “Inhomogeneous quadratic congruences,” *Functiones et Approximatio, Commentarii Mathematici*, vol. 47, no. 2. Adam Mickiewicz University Press, pp. 267–286, 2012.","short":"S. Baier, T.D. Browning, Functiones et Approximatio, Commentarii Mathematici 47 (2012) 267–286.","mla":"Baier, Stephan, and Timothy D. Browning. “Inhomogeneous Quadratic Congruences.” *Functiones et Approximatio, Commentarii Mathematici*, vol. 47, no. 2, Adam Mickiewicz University Press, 2012, pp. 267–86, doi:10.7169/facm/2012.47.2.9.","apa":"Baier, S., & Browning, T. D. (2012). Inhomogeneous quadratic congruences. *Functiones et Approximatio, Commentarii Mathematici*. Adam Mickiewicz University Press. https://doi.org/10.7169/facm/2012.47.2.9","ista":"Baier S, Browning TD. 2012. Inhomogeneous quadratic congruences. Functiones et Approximatio, Commentarii Mathematici. 47(2), 267–286.","ama":"Baier S, Browning TD. Inhomogeneous quadratic congruences. *Functiones et Approximatio, Commentarii Mathematici*. 2012;47(2):267-286. doi:10.7169/facm/2012.47.2.9"},"status":"public","month":"12","date_created":"2018-12-11T11:45:22Z","issue":"2","date_published":"2012-12-20T00:00:00Z","title":"Inhomogeneous quadratic congruences","acknowledgement":"EP/E053262/1\tEngineering and Physical Sciences Research Council","year":"2012","intvolume":" 47","quality_controlled":0,"publication":"Functiones et Approximatio, Commentarii Mathematici","volume":47,"date_updated":"2021-01-12T06:57:08Z","_id":"238","day":"20","publisher":"Adam Mickiewicz University Press","type":"journal_article","publist_id":"7666","doi":"10.7169/facm/2012.47.2.9","page":"267 - 286","publication_status":"published","abstract":[{"lang":"eng","text":"For given positive integers a, b, q we investigate the density of solutions (x, y) ∈ Z2 to congruences ax + by2 ≡ 0 mod q."}],"extern":1},{"extern":1,"type":"journal_article","publist_id":"4532","doi":"10.1063/1.3670747","abstract":[{"lang":"eng","text":"We study the BCS gap equation for a Fermi gas with unequal population of spin-up and spin-down states. For cosh (δ μ/T) ≤ 2, with T the temperature and δμ the chemical potential difference, the question of existence of non-trivial solutions can be reduced to spectral properties of a linear operator, similar to the unpolarized case studied previously in [Frank, R. L., Hainzl, C., Naboko, S., and Seiringer, R., J., Geom. Anal.17, 559-567 (2007)10.1007/BF02937429; Hainzl, C., Hamza, E., Seiringer, R., and Solovej, J. P., Commun., Math. Phys.281, 349-367 (2008)10.1007/s00220-008-0489-2; and Hainzl, C. and Seiringer, R., Phys. Rev. B77, 184517-110 435 (2008)]10.1103/PhysRevB.77.184517. For cosh (δ μ/T) > 2 the phase diagram is more complicated, however. We derive upper and lower bounds for the critical temperature, and study their behavior in the small coupling limit."}],"publication_status":"published","day":"01","publisher":"American Institute of Physics","volume":53,"date_updated":"2021-01-12T06:57:13Z","_id":"2394","year":"2012","publication":"Journal of Mathematical Physics","intvolume":" 53","quality_controlled":0,"title":"The gap equation for spin-polarized fermions","date_published":"2012-01-01T00:00:00Z","author":[{"full_name":"Freiji, Abraham","last_name":"Freiji","first_name":"Abraham"},{"full_name":"Hainzl, Christian","first_name":"Christian","last_name":"Hainzl"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","first_name":"Robert","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer"}],"status":"public","citation":{"short":"A. Freiji, C. Hainzl, R. Seiringer, Journal of Mathematical Physics 53 (2012).","ieee":"A. Freiji, C. Hainzl, and R. Seiringer, “The gap equation for spin-polarized fermions,” *Journal of Mathematical Physics*, vol. 53, no. 1. American Institute of Physics, 2012.","chicago":"Freiji, Abraham, Christian Hainzl, and Robert Seiringer. “The Gap Equation for Spin-Polarized Fermions.” *Journal of Mathematical Physics*. American Institute of Physics, 2012. https://doi.org/10.1063/1.3670747.","mla":"Freiji, Abraham, et al. “The Gap Equation for Spin-Polarized Fermions.” *Journal of Mathematical Physics*, vol. 53, no. 1, American Institute of Physics, 2012, doi:10.1063/1.3670747.","apa":"Freiji, A., Hainzl, C., & Seiringer, R. (2012). The gap equation for spin-polarized fermions. *Journal of Mathematical Physics*. American Institute of Physics. https://doi.org/10.1063/1.3670747","ista":"Freiji A, Hainzl C, Seiringer R. 2012. The gap equation for spin-polarized fermions. Journal of Mathematical Physics. 53(1).","ama":"Freiji A, Hainzl C, Seiringer R. The gap equation for spin-polarized fermions. *Journal of Mathematical Physics*. 2012;53(1). doi:10.1063/1.3670747"},"date_created":"2018-12-11T11:57:25Z","month":"01","issue":"1"},{"date_created":"2018-12-11T11:57:25Z","month":"01","issue":"3","status":"public","author":[{"last_name":"Frank","first_name":"Rupert","full_name":"Frank, Rupert L"},{"full_name":"Hainzl, Christian","first_name":"Christian","last_name":"Hainzl"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Robert Seiringer","orcid":"0000-0002-6781-0521","first_name":"Robert","last_name":"Seiringer"},{"last_name":"Solovej","first_name":"Jan","full_name":"Solovej, Jan P"}],"citation":{"apa":"Frank, R., Hainzl, C., Seiringer, R., & Solovej, J. (2012). Microscopic derivation of Ginzburg-Landau theory. *Journal of the American Mathematical Society*. American Mathematical Society. https://doi.org/10.1090/S0894-0347-2012-00735-8","ista":"Frank R, Hainzl C, Seiringer R, Solovej J. 2012. Microscopic derivation of Ginzburg-Landau theory. Journal of the American Mathematical Society. 25(3), 667–713.","ama":"Frank R, Hainzl C, Seiringer R, Solovej J. Microscopic derivation of Ginzburg-Landau theory. *Journal of the American Mathematical Society*. 2012;25(3):667-713. doi:10.1090/S0894-0347-2012-00735-8","chicago":"Frank, Rupert, Christian Hainzl, Robert Seiringer, and Jan Solovej. “Microscopic Derivation of Ginzburg-Landau Theory.” *Journal of the American Mathematical Society*. American Mathematical Society, 2012. https://doi.org/10.1090/S0894-0347-2012-00735-8.","ieee":"R. Frank, C. Hainzl, R. Seiringer, and J. Solovej, “Microscopic derivation of Ginzburg-Landau theory,” *Journal of the American Mathematical Society*, vol. 25, no. 3. American Mathematical Society, pp. 667–713, 2012.","short":"R. Frank, C. Hainzl, R. Seiringer, J. Solovej, Journal of the American Mathematical Society 25 (2012) 667–713.","mla":"Frank, Rupert, et al. “Microscopic Derivation of Ginzburg-Landau Theory.” *Journal of the American Mathematical Society*, vol. 25, no. 3, American Mathematical Society, 2012, pp. 667–713, doi:10.1090/S0894-0347-2012-00735-8."},"date_published":"2012-01-01T00:00:00Z","title":"Microscopic derivation of Ginzburg-Landau theory","intvolume":" 25","quality_controlled":0,"publication":"Journal of the American Mathematical Society","year":"2012","volume":25,"main_file_link":[{"url":"http://arxiv.org/abs/1102.4001","open_access":"1"}],"_id":"2395","date_updated":"2021-01-12T06:57:13Z","publisher":"American Mathematical Society","oa":1,"day":"01","page":"667 - 713","publication_status":"published","abstract":[{"lang":"eng","text":"We give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit is semiclassical in nature, and semiclassical analysis, with minimal regularity assumptions, plays an important part in our proof. "}],"type":"journal_article","publist_id":"4531","doi":"10.1090/S0894-0347-2012-00735-8","extern":1},{"issue":"3","month":"06","date_created":"2018-12-11T11:57:25Z","status":"public","citation":{"short":"B. Landon, R. Seiringer, Letters in Mathematical Physics 100 (2012) 237–243.","ieee":"B. Landon and R. Seiringer, “The scattering length at positive temperature,” *Letters in Mathematical Physics*, vol. 100, no. 3. Springer, pp. 237–243, 2012.","chicago":"Landon, Benjamin, and Robert Seiringer. “The Scattering Length at Positive Temperature.” *Letters in Mathematical Physics*. Springer, 2012. https://doi.org/10.1007/s11005-012-0566-5.","mla":"Landon, Benjamin, and Robert Seiringer. “The Scattering Length at Positive Temperature.” *Letters in Mathematical Physics*, vol. 100, no. 3, Springer, 2012, pp. 237–43, doi:10.1007/s11005-012-0566-5.","apa":"Landon, B., & Seiringer, R. (2012). The scattering length at positive temperature. *Letters in Mathematical Physics*. Springer. https://doi.org/10.1007/s11005-012-0566-5","ista":"Landon B, Seiringer R. 2012. The scattering length at positive temperature. Letters in Mathematical Physics. 100(3), 237–243.","ama":"Landon B, Seiringer R. The scattering length at positive temperature. *Letters in Mathematical Physics*. 2012;100(3):237-243. doi:10.1007/s11005-012-0566-5"},"author":[{"full_name":"Landon, Benjamin","first_name":"Benjamin","last_name":"Landon"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","last_name":"Seiringer","first_name":"Robert"}],"date_published":"2012-06-01T00:00:00Z","title":"The scattering length at positive temperature","intvolume":" 100","quality_controlled":0,"publication":"Letters in Mathematical Physics","year":"2012","_id":"2396","date_updated":"2021-01-12T06:57:13Z","main_file_link":[{"url":"http://arxiv.org/abs/1111.1683","open_access":"1"}],"volume":100,"publisher":"Springer","day":"01","oa":1,"publication_status":"published","abstract":[{"lang":"eng","text":"A positive temperature analogue of the scattering length of a potential V can be defined via integrating the difference of the heat kernels of -Δ and, with Δ the Laplacian. An upper bound on this quantity is a crucial input in the derivation of a bound on the critical temperature of a dilute Bose gas (Seiringer and Ueltschi in Phys Rev B 80:014502, 2009). In (Seiringer and Ueltschi in Phys Rev B 80:014502, 2009), a bound was given in the case of finite range potentials and sufficiently low temperature. In this paper, we improve the bound and extend it to potentials of infinite range."}],"page":"237 - 243","publist_id":"4529","doi":"10.1007/s11005-012-0566-5","type":"journal_article","extern":1},{"oa":1,"day":"01","publisher":"Springer","volume":100,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1105.1100"}],"_id":"2397","date_updated":"2021-01-12T06:57:14Z","extern":1,"type":"journal_article","doi":"10.1007/s11005-011-0535-4","publist_id":"4530","page":"119 - 138","abstract":[{"text":"We consider the low-density limit of a Fermi gas in the BCS approximation. We show that if the interaction potential allows for a two-particle bound state, the system at zero temperature is well approximated by the Gross-Pitaevskii functional, describing a Bose-Einstein condensate of fermion pairs.","lang":"eng"}],"publication_status":"published","date_published":"2012-05-01T00:00:00Z","citation":{"ista":"Hainzl C, Seiringer R. 2012. Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs. Letters in Mathematical Physics. 100(2), 119–138.","ama":"Hainzl C, Seiringer R. Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs. *Letters in Mathematical Physics*. 2012;100(2):119-138. doi:10.1007/s11005-011-0535-4","apa":"Hainzl, C., & Seiringer, R. (2012). Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs. *Letters in Mathematical Physics*. Springer. https://doi.org/10.1007/s11005-011-0535-4","mla":"Hainzl, Christian, and Robert Seiringer. “Low Density Limit of BCS Theory and Bose-Einstein Condensation of Fermion Pairs.” *Letters in Mathematical Physics*, vol. 100, no. 2, Springer, 2012, pp. 119–38, doi:10.1007/s11005-011-0535-4.","short":"C. Hainzl, R. Seiringer, Letters in Mathematical Physics 100 (2012) 119–138.","chicago":"Hainzl, Christian, and Robert Seiringer. “Low Density Limit of BCS Theory and Bose-Einstein Condensation of Fermion Pairs.” *Letters in Mathematical Physics*. Springer, 2012. https://doi.org/10.1007/s11005-011-0535-4.","ieee":"C. Hainzl and R. Seiringer, “Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs,” *Letters in Mathematical Physics*, vol. 100, no. 2. Springer, pp. 119–138, 2012."},"author":[{"full_name":"Hainzl, Christian","last_name":"Hainzl","first_name":"Christian"},{"full_name":"Robert Seiringer","orcid":"0000-0002-6781-0521","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"status":"public","date_created":"2018-12-11T11:57:25Z","month":"05","issue":"2","year":"2012","publication":"Letters in Mathematical Physics","quality_controlled":0,"intvolume":" 100","title":"Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs"},{"title":"Quantum hypothesis testing and non-equilibrium statistical mechanics","year":"2012","intvolume":" 24","quality_controlled":0,"publication":"Reviews in Mathematical Physics","month":"07","date_created":"2018-12-11T11:57:26Z","issue":"6","citation":{"ama":"Jakšić V, Ogata Y, Pillet C, Seiringer R. Quantum hypothesis testing and non-equilibrium statistical mechanics. *Reviews in Mathematical Physics*. 2012;24(6). doi:10.1142/S0129055X12300026","ista":"Jakšić V, Ogata Y, Pillet C, Seiringer R. 2012. Quantum hypothesis testing and non-equilibrium statistical mechanics. Reviews in Mathematical Physics. 24(6).","apa":"Jakšić, V., Ogata, Y., Pillet, C., & Seiringer, R. (2012). Quantum hypothesis testing and non-equilibrium statistical mechanics. *Reviews in Mathematical Physics*. World Scientific Publishing. https://doi.org/10.1142/S0129055X12300026","mla":"Jakšić, Vojkan, et al. “Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics.” *Reviews in Mathematical Physics*, vol. 24, no. 6, World Scientific Publishing, 2012, doi:10.1142/S0129055X12300026.","chicago":"Jakšić, Vojkan, Yoshiko Ogata, Claude Pillet, and Robert Seiringer. “Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics.” *Reviews in Mathematical Physics*. World Scientific Publishing, 2012. https://doi.org/10.1142/S0129055X12300026.","short":"V. Jakšić, Y. Ogata, C. Pillet, R. Seiringer, Reviews in Mathematical Physics 24 (2012).","ieee":"V. Jakšić, Y. Ogata, C. Pillet, and R. Seiringer, “Quantum hypothesis testing and non-equilibrium statistical mechanics,” *Reviews in Mathematical Physics*, vol. 24, no. 6. World Scientific Publishing, 2012."},"status":"public","author":[{"last_name":"Jakšić","first_name":"Vojkan","full_name":"Jakšić, Vojkan"},{"full_name":"Ogata, Yoshiko","last_name":"Ogata","first_name":"Yoshiko"},{"last_name":"Pillet","first_name":"Claude","full_name":"Pillet, Claude A"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Robert Seiringer","orcid":"0000-0002-6781-0521","first_name":"Robert","last_name":"Seiringer"}],"date_published":"2012-07-01T00:00:00Z","publication_status":"published","abstract":[{"text":"We extend the mathematical theory of quantum hypothesis testing to the general W*-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time.","lang":"eng"}],"type":"review","publist_id":"4528","doi":"10.1142/S0129055X12300026","extern":1,"volume":24,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1109.3804"}],"_id":"2398","date_updated":"2020-07-14T12:45:40Z","publisher":"World Scientific Publishing","oa":1,"day":"01"},{"alternative_title":["Lecture Notes in Mathematics"],"quality_controlled":0,"intvolume":" 2051","publication":"Quantum Many Body Systems","year":"2012","title":"Cold quantum gases and bose einstein condensation","editor":[{"full_name":"Rivasseau, Vincent","first_name":"Vincent","last_name":"Rivasseau"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","last_name":"Seiringer","full_name":"Robert Seiringer","orcid":"0000-0002-6781-0521"},{"last_name":"Solovej","first_name":"Jan","full_name":"Solovej, Jan P"},{"full_name":"Spencer, Thomas","first_name":"Thomas","last_name":"Spencer"}],"date_published":"2012-01-01T00:00:00Z","author":[{"last_name":"Seiringer","first_name":"Robert","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"citation":{"short":"R. Seiringer, in:, V. Rivasseau, R. Seiringer, J. Solovej, T. Spencer (Eds.), Quantum Many Body Systems, Springer, 2012, pp. 55–92.","chicago":"Seiringer, Robert. “Cold Quantum Gases and Bose Einstein Condensation.” In *Quantum Many Body Systems*, edited by Vincent Rivasseau, Robert Seiringer, Jan Solovej, and Thomas Spencer, 2051:55–92. Springer, 2012. https://doi.org/10.1007/978-3-642-29511-9_2.","ieee":"R. Seiringer, “Cold quantum gases and bose einstein condensation,” in *Quantum Many Body Systems*, vol. 2051, V. Rivasseau, R. Seiringer, J. Solovej, and T. Spencer, Eds. Springer, 2012, pp. 55–92.","mla":"Seiringer, Robert. “Cold Quantum Gases and Bose Einstein Condensation.” *Quantum Many Body Systems*, edited by Vincent Rivasseau et al., vol. 2051, Springer, 2012, pp. 55–92, doi:10.1007/978-3-642-29511-9_2.","apa":"Seiringer, R. (2012). Cold quantum gases and bose einstein condensation. In V. Rivasseau, R. Seiringer, J. Solovej, & T. Spencer (Eds.), *Quantum Many Body Systems* (Vol. 2051, pp. 55–92). Springer. https://doi.org/10.1007/978-3-642-29511-9_2","ista":"Seiringer R. 2012.Cold quantum gases and bose einstein condensation. In: Quantum Many Body Systems. Lecture Notes in Mathematics, vol. 2051, 55–92.","ama":"Seiringer R. Cold quantum gases and bose einstein condensation. In: Rivasseau V, Seiringer R, Solovej J, Spencer T, eds. *Quantum Many Body Systems*. Vol 2051. Springer; 2012:55-92. doi:10.1007/978-3-642-29511-9_2"},"status":"public","date_created":"2018-12-11T11:57:26Z","month":"01","extern":1,"type":"book_chapter","publist_id":"4526","doi":"10.1007/978-3-642-29511-9_2","page":"55 - 92","abstract":[{"lang":"eng","text":"Bose–Einstein condensation (BEC) in cold atomic gases was first achieved experimentally in 1995 [1, 6]. After initial failed attempts with spin-polarized atomic hydrogen, the first successful demonstrations of this phenomenon used gases of rubidium and sodium atoms, respectively. Since then there has been a surge of activity in this field, with ingenious experiments putting forth more and more astonishing results about the behavior of matter at very cold temperatures.\n"}],"publication_status":"published","day":"01","publisher":"Springer","volume":2051,"date_updated":"2021-01-12T06:57:14Z","_id":"2399"},{"doi":"10.1080/10586458.2011.605733","publist_id":"7664","type":"journal_article","publication_status":"published","abstract":[{"text":"We investigate the frequency of positive squareful numbers x, y, z≤B for which x+y=z and present a conjecture concerning its asymptotic behavior.","lang":"eng"}],"page":"204 - 211","extern":1,"date_updated":"2021-01-12T06:57:15Z","_id":"240","volume":21,"day":"23","publisher":"Taylor & Francis","title":"Sums of three squareful numbers","acknowledgement":"EP/E053262/1\tEngineering and Physical Sciences Research Council","publication":"Experimental Mathematics","intvolume":" 21","year":"2012","quality_controlled":0,"author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Timothy Browning","last_name":"Browning","first_name":"Timothy D"},{"full_name":"Valckenborgh, K Van","last_name":"Valckenborgh","first_name":"K Van"}],"citation":{"apa":"Browning, T. D., & Valckenborgh, K. V. (2012). Sums of three squareful numbers. *Experimental Mathematics*. Taylor & Francis. https://doi.org/10.1080/10586458.2011.605733","ista":"Browning TD, Valckenborgh KV. 2012. Sums of three squareful numbers. Experimental Mathematics. 21(2), 204–211.","ama":"Browning TD, Valckenborgh KV. Sums of three squareful numbers. *Experimental Mathematics*. 2012;21(2):204-211. doi:10.1080/10586458.2011.605733","short":"T.D. Browning, K.V. Valckenborgh, Experimental Mathematics 21 (2012) 204–211.","ieee":"T. D. Browning and K. V. Valckenborgh, “Sums of three squareful numbers,” *Experimental Mathematics*, vol. 21, no. 2. Taylor & Francis, pp. 204–211, 2012.","chicago":"Browning, Timothy D, and K Van Valckenborgh. “Sums of Three Squareful Numbers.” *Experimental Mathematics*. Taylor & Francis, 2012. https://doi.org/10.1080/10586458.2011.605733.","mla":"Browning, Timothy D., and K. Van Valckenborgh. “Sums of Three Squareful Numbers.” *Experimental Mathematics*, vol. 21, no. 2, Taylor & Francis, 2012, pp. 204–11, doi:10.1080/10586458.2011.605733."},"status":"public","issue":"2","month":"05","date_created":"2018-12-11T11:45:23Z","date_published":"2012-05-23T00:00:00Z"},{"publisher":"Springer","oa":1,"day":"01","volume":313,"main_file_link":[{"url":"http://arxiv.org/abs/1106.0729","open_access":"1"}],"date_updated":"2021-01-12T06:57:15Z","_id":"2400","extern":1,"page":"405 - 424","publication_status":"published","abstract":[{"text":"If the polaron coupling constant α is large enough, bipolarons or multi-polarons will form. When passing through the critical α c from above, does the radius of the system simply get arbitrarily large or does it reach a maximum and then explode? We prove that it is always the latter. We also prove the analogous statement for the Pekar-Tomasevich (PT) approximation to the energy, in which case there is a solution to the PT equation at α c. Similarly, we show that the same phenomenon occurs for atoms, e. g., helium, at the critical value of the nuclear charge. Our proofs rely only on energy estimates, not on a detailed analysis of the Schrödinger equation, and are very general. They use the fact that the Coulomb repulsion decays like 1/r, while 'uncertainty principle' localization energies decay more rapidly, as 1/r 2.","lang":"eng"}],"type":"journal_article","publist_id":"4527","doi":"10.1007/s00220-012-1436-9","date_published":"2012-07-01T00:00:00Z","date_created":"2018-12-11T11:57:27Z","month":"07","issue":"2","status":"public","citation":{"ieee":"R. Frank, É. Lieb, and R. Seiringer, “Binding of polarons and atoms at threshold,” *Communications in Mathematical Physics*, vol. 313, no. 2. Springer, pp. 405–424, 2012.","short":"R. Frank, É. Lieb, R. Seiringer, Communications in Mathematical Physics 313 (2012) 405–424.","chicago":"Frank, Rupert, Élliott Lieb, and Robert Seiringer. “Binding of Polarons and Atoms at Threshold.” *Communications in Mathematical Physics*. Springer, 2012. https://doi.org/10.1007/s00220-012-1436-9.","mla":"Frank, Rupert, et al. “Binding of Polarons and Atoms at Threshold.” *Communications in Mathematical Physics*, vol. 313, no. 2, Springer, 2012, pp. 405–24, doi:10.1007/s00220-012-1436-9.","apa":"Frank, R., Lieb, É., & Seiringer, R. (2012). Binding of polarons and atoms at threshold. *Communications in Mathematical Physics*. Springer. https://doi.org/10.1007/s00220-012-1436-9","ama":"Frank R, Lieb É, Seiringer R. Binding of polarons and atoms at threshold. *Communications in Mathematical Physics*. 2012;313(2):405-424. doi:10.1007/s00220-012-1436-9","ista":"Frank R, Lieb É, Seiringer R. 2012. Binding of polarons and atoms at threshold. Communications in Mathematical Physics. 313(2), 405–424."},"author":[{"full_name":"Frank, Rupert L","last_name":"Frank","first_name":"Rupert"},{"first_name":"Élliott","last_name":"Lieb","full_name":"Lieb, Élliott H"},{"orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"publication":"Communications in Mathematical Physics","year":"2012","quality_controlled":0,"intvolume":" 313","title":"Binding of polarons and atoms at threshold"}]