[{"author":[{"full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D"}],"publist_id":"7704","title":"Sums of four biquadrates","citation":{"mla":"Browning, Timothy D. “Sums of Four Biquadrates.” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 134, no. 3, Cambridge University Press, 2003, pp. 385–95, doi:10.1017/S0305004102006382.","ieee":"T. D. Browning, “Sums of four biquadrates,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 134, no. 3. Cambridge University Press, pp. 385–395, 2003.","short":"T.D. Browning, Mathematical Proceedings of the Cambridge Philosophical Society 134 (2003) 385–395.","ama":"Browning TD. Sums of four biquadrates. Mathematical Proceedings of the Cambridge Philosophical Society. 2003;134(3):385-395. doi:10.1017/S0305004102006382","apa":"Browning, T. D. (2003). Sums of four biquadrates. Mathematical Proceedings of the Cambridge Philosophical Society. Cambridge University Press. https://doi.org/10.1017/S0305004102006382","chicago":"Browning, Timothy D. “Sums of Four Biquadrates.” Mathematical Proceedings of the Cambridge Philosophical Society. Cambridge University Press, 2003. https://doi.org/10.1017/S0305004102006382.","ista":"Browning TD. 2003. Sums of four biquadrates. Mathematical Proceedings of the Cambridge Philosophical Society. 134(3), 385–395."},"date_updated":"2021-01-12T06:55:07Z","extern":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","status":"public","_id":"207","page":"385 - 395","issue":"3","date_published":"2003-05-01T00:00:00Z","volume":134,"doi":"10.1017/S0305004102006382","date_created":"2018-12-11T11:45:12Z","year":"2003","publication_status":"published","day":"01","language":[{"iso":"eng"}],"publication":"Mathematical Proceedings of the Cambridge Philosophical Society","quality_controlled":"1","publisher":"Cambridge University Press","month":"05","intvolume":" 134","oa_version":"None"},{"_id":"208","status":"public","type":"journal_article","extern":1,"date_updated":"2021-01-12T06:55:10Z","citation":{"mla":"Browning, Timothy D. “Counting Rational Points on Diagonal Quadratic Surfaces.” Quarterly Journal of Mathematics, vol. 54, no. 1, Oxford University Press, 2003, pp. 11–31, doi:10.1093/qjmath/54.1.11.","ama":"Browning TD. Counting rational points on diagonal quadratic surfaces. Quarterly Journal of Mathematics. 2003;54(1):11-31. doi:10.1093/qjmath/54.1.11","apa":"Browning, T. D. (2003). Counting rational points on diagonal quadratic surfaces. Quarterly Journal of Mathematics. Oxford University Press. https://doi.org/10.1093/qjmath/54.1.11","ieee":"T. D. Browning, “Counting rational points on diagonal quadratic surfaces,” Quarterly Journal of Mathematics, vol. 54, no. 1. Oxford University Press, pp. 11–31, 2003.","short":"T.D. Browning, Quarterly Journal of Mathematics 54 (2003) 11–31.","chicago":"Browning, Timothy D. “Counting Rational Points on Diagonal Quadratic Surfaces.” Quarterly Journal of Mathematics. Oxford University Press, 2003. https://doi.org/10.1093/qjmath/54.1.11.","ista":"Browning TD. 2003. Counting rational points on diagonal quadratic surfaces. Quarterly Journal of Mathematics. 54(1), 11–31."},"title":"Counting rational points on diagonal quadratic surfaces","author":[{"full_name":"Timothy Browning","orcid":"0000-0002-8314-0177","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D"}],"publist_id":"7705","abstract":[{"text":"For any ε > 0 and any diagonal quadratic form Q ∈ ℤ[x 1, x 2, x 3, x 4] with a square-free discriminant of modulus Δ Q ≠ 0, we establish the uniform estimate ≪ε B 3/2+ε + B 2+ε/Δ Q 1/6 for the number of rational points of height at most B lying in the projective surface Q = 0.","lang":"eng"}],"intvolume":" 54","month":"03","quality_controlled":0,"publisher":"Oxford University Press","publication":"Quarterly Journal of Mathematics","day":"01","publication_status":"published","year":"2003","date_created":"2018-12-11T11:45:13Z","issue":"1","volume":54,"doi":"10.1093/qjmath/54.1.11","date_published":"2003-03-01T00:00:00Z","page":"11 - 31"},{"author":[{"first_name":"Élliott","full_name":"Lieb, Élliott H","last_name":"Lieb"},{"full_name":"Robert Seiringer","orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"publist_id":"4589","title":"Bose-Einstein condensation of dilute gases in traps ","editor":[{"first_name":"Yulia","full_name":"Karpeshina, Yulia","last_name":"Karpeshina"},{"first_name":"Rudi","full_name":"Weikard, Rudi","last_name":"Weikard"},{"first_name":"Yanni","last_name":"Zeng","full_name":"Zeng, Yanni"}],"citation":{"mla":"Lieb, Élliott, and Robert Seiringer. Bose-Einstein Condensation of Dilute Gases in Traps . Edited by Yulia Karpeshina et al., vol. 327, American Mathematical Society, 2003, pp. 239–50, doi:10.1090/conm/327/05818.","short":"É. Lieb, R. Seiringer, in:, Y. Karpeshina, R. Weikard, Y. Zeng (Eds.), American Mathematical Society, 2003, pp. 239–250.","ieee":"É. Lieb and R. Seiringer, “Bose-Einstein condensation of dilute gases in traps ,” presented at the Differential Equations and Mathematical Physics, 2003, vol. 327, pp. 239–250.","ama":"Lieb É, Seiringer R. Bose-Einstein condensation of dilute gases in traps . In: Karpeshina Y, Weikard R, Zeng Y, eds. Vol 327. American Mathematical Society; 2003:239-250. doi:10.1090/conm/327/05818","apa":"Lieb, É., & Seiringer, R. (2003). Bose-Einstein condensation of dilute gases in traps . In Y. Karpeshina, R. Weikard, & Y. Zeng (Eds.) (Vol. 327, pp. 239–250). Presented at the Differential Equations and Mathematical Physics, American Mathematical Society. https://doi.org/10.1090/conm/327/05818","chicago":"Lieb, Élliott, and Robert Seiringer. “Bose-Einstein Condensation of Dilute Gases in Traps .” edited by Yulia Karpeshina, Rudi Weikard, and Yanni Zeng, 327:239–50. American Mathematical Society, 2003. https://doi.org/10.1090/conm/327/05818.","ista":"Lieb É, Seiringer R. 2003. Bose-Einstein condensation of dilute gases in traps . Differential Equations and Mathematical Physics, Contemporary Mathematics, vol. 327, 239–250."},"date_updated":"2021-01-12T06:56:52Z","extern":1,"conference":{"name":"Differential Equations and Mathematical Physics"},"type":"conference","status":"public","_id":"2337","page":"239 - 250","date_created":"2018-12-11T11:57:04Z","doi":"10.1090/conm/327/05818","volume":327,"date_published":"2003-01-01T00:00:00Z","year":"2003","publication_status":"published","day":"01","oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0210028","open_access":"1"}],"quality_controlled":0,"publisher":"American Mathematical Society","alternative_title":["Contemporary Mathematics"],"intvolume":" 327","month":"01"},{"date_created":"2018-12-11T11:57:11Z","issue":"3","doi":"10.4007/annals.2003.158.1067 ","date_published":"2003-11-01T00:00:00Z","volume":158,"page":"1067 - 1080","publication":"Annals of Mathematics","day":"01","year":"2003","publication_status":"published","intvolume":" 158","month":"11","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math/0205088"}],"oa":1,"publisher":"Princeton University Press","quality_controlled":0,"abstract":[{"lang":"eng","text":"The classic Poincaré inequality bounds the L q-norm of a function f in a bounded domain Ω ⊂ ℝ n in terms of some L p-norm of its gradient in Ω. We generalize this in two ways: In the first generalization we remove a set Τ from Ω and concentrate our attention on Λ = Ω \\ Τ. This new domain might not even be connected and hence no Poincaré inequality can generally hold for it, or if it does hold it might have a very bad constant. This is so even if the volume of Τ is arbitrarily small. A Poincaré inequality does hold, however, if one makes the additional assumption that f has a finite L p gradient norm on the whole of Ω, not just on Λ. The important point is that the Poincaré inequality thus obtained bounds the L q-norm of f in terms of the L p gradient norm on Λ (not Ω) plus an additional term that goes to zero as the volume of Τ goes to zero. This error term depends on Τ only through its volume. Apart from this additive error term, the constant in the inequality remains that of the 'nice' domain Ω. In the second generalization we are given a vector field A and replace ∇ by ∇ + iA(x) (geometrically, a connection on a U(1) bundle). Unlike the A = 0 case, the infimum of ∥(∇ + iA)f∥ p over all f with a given ∥f∥ q is in general not zero. This permits an improvement of the inequality by the addition of a term whose sharp value we derive. We describe some open problems that arise from these generalizations."}],"title":"Poincaré inequalities in punctured domains","author":[{"first_name":"Élliott","last_name":"Lieb","full_name":"Lieb, Élliott H"},{"full_name":"Robert Seiringer","orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"},{"last_name":"Yngvason","full_name":"Yngvason, Jakob","first_name":"Jakob"}],"publist_id":"4570","extern":1,"date_updated":"2021-01-12T06:57:00Z","citation":{"ama":"Lieb É, Seiringer R, Yngvason J. Poincaré inequalities in punctured domains. Annals of Mathematics. 2003;158(3):1067-1080. doi:10.4007/annals.2003.158.1067 ","apa":"Lieb, É., Seiringer, R., & Yngvason, J. (2003). Poincaré inequalities in punctured domains. Annals of Mathematics. Princeton University Press. https://doi.org/10.4007/annals.2003.158.1067 ","ieee":"É. Lieb, R. Seiringer, and J. Yngvason, “Poincaré inequalities in punctured domains,” Annals of Mathematics, vol. 158, no. 3. Princeton University Press, pp. 1067–1080, 2003.","short":"É. Lieb, R. Seiringer, J. Yngvason, Annals of Mathematics 158 (2003) 1067–1080.","mla":"Lieb, Élliott, et al. “Poincaré Inequalities in Punctured Domains.” Annals of Mathematics, vol. 158, no. 3, Princeton University Press, 2003, pp. 1067–80, doi:10.4007/annals.2003.158.1067 .","ista":"Lieb É, Seiringer R, Yngvason J. 2003. Poincaré inequalities in punctured domains. Annals of Mathematics. 158(3), 1067–1080.","chicago":"Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “Poincaré Inequalities in Punctured Domains.” Annals of Mathematics. Princeton University Press, 2003. https://doi.org/10.4007/annals.2003.158.1067 ."},"status":"public","type":"journal_article","_id":"2357"},{"status":"public","type":"journal_article","_id":"2354","title":"Ground state asymptotics of a dilute, rotating gas","author":[{"last_name":"Seiringer","full_name":"Robert Seiringer","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"publist_id":"4572","extern":1,"citation":{"chicago":"Seiringer, Robert. “Ground State Asymptotics of a Dilute, Rotating Gas.” Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd., 2003. https://doi.org/10.1088/0305-4470/36/37/312.","ista":"Seiringer R. 2003. Ground state asymptotics of a dilute, rotating gas. Journal of Physics A: Mathematical and Theoretical. 36(37), 9755–9778.","mla":"Seiringer, Robert. “Ground State Asymptotics of a Dilute, Rotating Gas.” Journal of Physics A: Mathematical and Theoretical, vol. 36, no. 37, IOP Publishing Ltd., 2003, pp. 9755–78, doi:10.1088/0305-4470/36/37/312.","ama":"Seiringer R. Ground state asymptotics of a dilute, rotating gas. Journal of Physics A: Mathematical and Theoretical. 2003;36(37):9755-9778. doi:10.1088/0305-4470/36/37/312","apa":"Seiringer, R. (2003). Ground state asymptotics of a dilute, rotating gas. Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd. https://doi.org/10.1088/0305-4470/36/37/312","short":"R. Seiringer, Journal of Physics A: Mathematical and Theoretical 36 (2003) 9755–9778.","ieee":"R. Seiringer, “Ground state asymptotics of a dilute, rotating gas,” Journal of Physics A: Mathematical and Theoretical, vol. 36, no. 37. IOP Publishing Ltd., pp. 9755–9778, 2003."},"date_updated":"2021-01-12T06:56:59Z","month":"09","intvolume":" 36","publisher":"IOP Publishing Ltd.","quality_controlled":0,"oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0306022","open_access":"1"}],"abstract":[{"lang":"eng","text":"We investigate the ground state properties of a gas of interacting particles confined in an external potential in three dimensions and subject to rotation around an axis of symmetry. We consider the Gross-Pitaevskii (GP) limit of a dilute gas. Analysing both the absolute and the bosonic ground states of the system, we show, in particular, their different behaviour for a certain range of parameters. This parameter range is determined by the question whether the rotational symmetry in the minimizer of the GP functional is broken or not. For the absolute ground state, we prove that in the GP limit a modified GP functional depending on density matrices correctly describes the energy and reduced density matrices, independent of symmetry breaking. For the bosonic ground state this holds true if and only if the symmetry is unbroken."}],"volume":36,"doi":"10.1088/0305-4470/36/37/312","date_published":"2003-09-19T00:00:00Z","issue":"37","date_created":"2018-12-11T11:57:10Z","page":"9755 - 9778","day":"19","publication":"Journal of Physics A: Mathematical and Theoretical","publication_status":"published","year":"2003"}]