[{"publication":"Quarterly Journal of Mathematics","year":"2003","date_published":"2003-03-01T00:00:00Z","publisher":"Oxford University Press","title":"Counting rational points on diagonal quadratic surfaces","extern":1,"intvolume":" 54","author":[{"full_name":"Timothy Browning","first_name":"Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2019-04-26T07:22:07Z","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"}],"status":"public","publist_id":"7705","quality_controlled":0,"issue":"1","page":"11 - 31","_id":"208","citation":{"chicago":"Browning, Timothy D. “Counting Rational Points on Diagonal Quadratic Surfaces.” *Quarterly Journal of Mathematics* 54, no. 1 (2003): 11–31. https://doi.org/10.1093/qjmath/54.1.11.","apa":"Browning, T. D. (2003). Counting rational points on diagonal quadratic surfaces. *Quarterly Journal of Mathematics*, *54*(1), 11–31. https://doi.org/10.1093/qjmath/54.1.11","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.","short":"T.D. Browning, Quarterly Journal of Mathematics 54 (2003) 11–31.","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","ieee":"T. D. Browning, “Counting rational points on diagonal quadratic surfaces,” *Quarterly Journal of Mathematics*, vol. 54, no. 1, pp. 11–31, 2003.","ista":"Browning TD. 2003. Counting rational points on diagonal quadratic surfaces. Quarterly Journal of Mathematics. 54(1), 11–31."},"volume":54,"publication_status":"published","day":"01","month":"03","date_created":"2018-12-11T11:45:13Z","type":"journal_article","doi":"10.1093/qjmath/54.1.11"},{"date_updated":"2020-07-14T12:45:39Z","quality_controlled":0,"oa":1,"publist_id":"4589","status":"public","title":"Bose-Einstein condensation of dilute gases in traps ","date_published":"2003-01-01T00:00:00Z","publisher":"American Mathematical Society","year":"2003","editor":[{"full_name":"Karpeshina, Yulia","first_name":"Yulia","last_name":"Karpeshina"},{"first_name":"Rudi","full_name":"Weikard, Rudi","last_name":"Weikard"},{"full_name":"Zeng, Yanni","first_name":"Yanni","last_name":"Zeng"}],"author":[{"last_name":"Lieb","full_name":"Lieb, Élliott H","first_name":"Élliott"},{"full_name":"Robert Seiringer","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521"}],"conference":{"name":"Differential Equations and Mathematical Physics"},"extern":1,"intvolume":" 327","type":"conference","date_created":"2018-12-11T11:57:04Z","alternative_title":["Contemporary Mathematics"],"month":"01","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0210028"}],"doi":"10.1090/conm/327/05818","_id":"2337","page":"239 - 250","day":"01","publication_status":"published","volume":327,"citation":{"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.","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","short":"É. Lieb, R. Seiringer, in:, Y. Karpeshina, R. Weikard, Y. Zeng (Eds.), American Mathematical Society, 2003, pp. 239–250.","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.","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.","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"}},{"doi":"10.1088/0305-4470/36/37/312","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0306022"}],"month":"09","date_created":"2018-12-11T11:57:10Z","type":"journal_article","citation":{"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.","chicago":"Seiringer, Robert. “Ground State Asymptotics of a Dilute, Rotating Gas.” *Journal of Physics A: Mathematical and Theoretical* 36, no. 37 (2003): 9755–78. https://doi.org/10.1088/0305-4470/36/37/312.","short":"R. Seiringer, Journal of Physics A: Mathematical and Theoretical 36 (2003) 9755–9778.","apa":"Seiringer, R. (2003). Ground state asymptotics of a dilute, rotating gas. *Journal of Physics A: Mathematical and Theoretical*, *36*(37), 9755–9778. https://doi.org/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","ieee":"R. Seiringer, “Ground state asymptotics of a dilute, rotating gas,” *Journal of Physics A: Mathematical and Theoretical*, vol. 36, no. 37, pp. 9755–9778, 2003.","ista":"Seiringer R. 2003. Ground state asymptotics of a dilute, rotating gas. Journal of Physics A: Mathematical and Theoretical. 36(37), 9755–9778."},"volume":36,"publication_status":"published","day":"19","issue":"37","page":"9755 - 9778","_id":"2354","abstract":[{"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.","lang":"eng"}],"status":"public","publist_id":"4572","quality_controlled":0,"oa":1,"date_updated":"2020-07-14T12:45:39Z","extern":1,"intvolume":" 36","author":[{"orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","first_name":"Robert","full_name":"Robert Seiringer"}],"year":"2003","publication":"Journal of Physics A: Mathematical and Theoretical","date_published":"2003-09-19T00:00:00Z","publisher":"IOP Publishing Ltd.","title":"Ground state asymptotics of a dilute, rotating gas"},{"date_updated":"2020-07-14T12:45:39Z","abstract":[{"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.","lang":"eng"}],"status":"public","publist_id":"4570","oa":1,"quality_controlled":0,"year":"2003","publication":"Annals of Mathematics","publisher":"Princeton University Press","date_published":"2003-11-01T00:00:00Z","title":"Poincaré inequalities in punctured domains","extern":1,"intvolume":" 158","author":[{"first_name":"Élliott","full_name":"Lieb, Élliott H","last_name":"Lieb"},{"orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Robert Seiringer","last_name":"Seiringer"},{"last_name":"Yngvason","full_name":"Yngvason, Jakob","first_name":"Jakob"}],"main_file_link":[{"url":"http://arxiv.org/abs/math/0205088","open_access":"1"}],"month":"11","date_created":"2018-12-11T11:57:11Z","type":"journal_article","doi":"10.4007/annals.2003.158.1067 ","page":"1067 - 1080","issue":"3","_id":"2357","citation":{"apa":"Lieb, É., Seiringer, R., & Yngvason, J. (2003). Poincaré inequalities in punctured domains. *Annals of Mathematics*, *158*(3), 1067–1080. https://doi.org/10.4007/annals.2003.158.1067 ","short":"É. Lieb, R. Seiringer, J. Yngvason, Annals of Mathematics 158 (2003) 1067–1080.","chicago":"Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “Poincaré Inequalities in Punctured Domains.” *Annals of Mathematics* 158, no. 3 (2003): 1067–80. https://doi.org/10.4007/annals.2003.158.1067 .","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 .","ieee":"É. Lieb, R. Seiringer, and J. Yngvason, “Poincaré inequalities in punctured domains,” *Annals of Mathematics*, vol. 158, no. 3, pp. 1067–1080, 2003.","ista":"Lieb É, Seiringer R, Yngvason J. 2003. Poincaré inequalities in punctured domains. Annals of Mathematics. 158(3), 1067–1080.","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 "},"volume":158,"publication_status":"published","day":"01"},{"date_updated":"2020-07-14T12:45:39Z","quality_controlled":0,"oa":1,"publist_id":"4571","status":"public","abstract":[{"lang":"eng","text":"A study was conducted on the one-dimensional (1D) bosons in three-dimensional (3D) traps. A rigorous analysis was carried out on the parameter regions in which various types of 1D or 3D behavior occurred in the ground state. The four parameter regions include density, transverse, longitudinal dimensions and scattering length."}],"title":"One-dimensional Bosons in three-dimensional traps","publisher":"American Physical Society","date_published":"2003-10-10T00:00:00Z","publication":"Physical Review Letters","year":"2003","author":[{"full_name":"Lieb, Élliott H","first_name":"Élliott","last_name":"Lieb"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Robert Seiringer","last_name":"Seiringer"},{"last_name":"Yngvason","first_name":"Jakob","full_name":"Yngvason, Jakob"}],"intvolume":" 91","extern":1,"type":"journal_article","date_created":"2018-12-11T11:57:12Z","main_file_link":[{"url":"http://arxiv.org/abs/cond-mat/0304071","open_access":"1"}],"month":"10","doi":"10.1103/PhysRevLett.91.150401","_id":"2358","page":"1504011 - 1504014","issue":"15","day":"10","publication_status":"published","volume":91,"citation":{"chicago":"Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “One-Dimensional Bosons in Three-Dimensional Traps.” *Physical Review Letters* 91, no. 15 (2003): 1504011–14. https://doi.org/10.1103/PhysRevLett.91.150401.","mla":"Lieb, Élliott, et al. “One-Dimensional Bosons in Three-Dimensional Traps.” *Physical Review Letters*, vol. 91, no. 15, American Physical Society, 2003, pp. 1504011–14, doi:10.1103/PhysRevLett.91.150401.","short":"É. Lieb, R. Seiringer, J. Yngvason, Physical Review Letters 91 (2003) 1504011–1504014.","apa":"Lieb, É., Seiringer, R., & Yngvason, J. (2003). One-dimensional Bosons in three-dimensional traps. *Physical Review Letters*, *91*(15), 1504011–1504014. https://doi.org/10.1103/PhysRevLett.91.150401","ama":"Lieb É, Seiringer R, Yngvason J. One-dimensional Bosons in three-dimensional traps. *Physical Review Letters*. 2003;91(15):1504011-1504014. doi:10.1103/PhysRevLett.91.150401","ieee":"É. Lieb, R. Seiringer, and J. Yngvason, “One-dimensional Bosons in three-dimensional traps,” *Physical Review Letters*, vol. 91, no. 15, pp. 1504011–1504014, 2003.","ista":"Lieb É, Seiringer R, Yngvason J. 2003. One-dimensional Bosons in three-dimensional traps. Physical Review Letters. 91(15), 1504011–1504014."}}]