[{"publication_status":"published","volume":132,"month":"04","title":"Counting rational points on algebraic varieties","date_published":"2006-04-15T00:00:00Z","publisher":"Unknown","quality_controlled":0,"doi":"10.1215/S0012-7094-06-13236-2","abstract":[{"text":"For any N ≥ 2, let Z ⊂ ℙN be a geometrically integral algebraic variety of degree d. This article is concerned with the number Nz(B) of ℚ-rational points on Z which have height at most B. For any ε > 0, we establish the estimate NZ(B) = O d,ε,N(Bdim Z+ε), provided that d ≥ 6. As indicated, the implied constant depends at most on d, ε, and N.","lang":"eng"}],"publication":"Duke Mathematical Journal","citation":{"chicago":"Browning, Timothy D, Roger Heath Brown, and Per Salberger. “Counting Rational Points on Algebraic Varieties.” *Duke Mathematical Journal* 132, no. 3 (2006): 545–78. https://doi.org/10.1215/S0012-7094-06-13236-2.","short":"T.D. Browning, R. Heath Brown, P. Salberger, Duke Mathematical Journal 132 (2006) 545–578.","mla":"Browning, Timothy D., et al. “Counting Rational Points on Algebraic Varieties.” *Duke Mathematical Journal*, vol. 132, no. 3, Unknown, 2006, pp. 545–78, doi:10.1215/S0012-7094-06-13236-2.","ista":"Browning TD, Heath Brown R, Salberger P. 2006. Counting rational points on algebraic varieties. Duke Mathematical Journal. 132(3), 545–578.","ieee":"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.","ama":"Browning TD, Heath Brown R, Salberger P. Counting rational points on algebraic varieties. *Duke Mathematical Journal*. 2006;132(3):545-578. doi:10.1215/S0012-7094-06-13236-2","apa":"Browning, T. D., Heath Brown, R., & Salberger, P. (2006). Counting rational points on algebraic varieties. *Duke Mathematical Journal*, *132*(3), 545–578. https://doi.org/10.1215/S0012-7094-06-13236-2"},"status":"public","intvolume":" 132","extern":1,"author":[{"full_name":"Timothy Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D","last_name":"Browning"},{"first_name":"Roger","last_name":"Heath Brown","full_name":"Heath-Brown, Roger"},{"last_name":"Salberger","first_name":"Per","full_name":"Salberger, Per"}],"_id":"216","type":"journal_article","date_updated":"2019-04-26T07:22:09Z","issue":"3","date_created":"2018-12-11T11:45:15Z","page":"545 - 578","year":"2006","day":"15","publist_id":"7696"},{"_id":"218","type":"journal_article","author":[{"full_name":"de la Bretèche, Régis","first_name":"Régis","last_name":"De La Bretèche"},{"last_name":"Browning","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Timothy Browning"}],"date_updated":"2019-04-26T07:22:09Z","extern":1,"intvolume":" 125","publist_id":"7694","year":"2006","day":"01","page":"291 - 304","date_created":"2018-12-11T11:45:16Z","issue":"3","volume":125,"publication_status":"published","status":"public","citation":{"ama":"De La Bretèche R, Browning TD. Sums of arithmetic functions over values of binary forms. *Acta Arithmetica*. 2006;125(3):291-304. doi:10.4064/aa125-3-6","apa":"De La Bretèche, R., & Browning, T. D. (2006). Sums of arithmetic functions over values of binary forms. *Acta Arithmetica*, *125*(3), 291–304. https://doi.org/10.4064/aa125-3-6","short":"R. De La Bretèche, T.D. Browning, Acta Arithmetica 125 (2006) 291–304.","ista":"De La Bretèche R, Browning TD. 2006. Sums of arithmetic functions over values of binary forms. Acta Arithmetica. 125(3), 291–304.","mla":"De La Bretèche, Régis, and Timothy D. Browning. “Sums of Arithmetic Functions over Values of Binary Forms.” *Acta Arithmetica*, vol. 125, no. 3, Instytut Matematyczny, 2006, pp. 291–304, doi:10.4064/aa125-3-6.","ieee":"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.","chicago":"De La Bretèche, Régis, and Timothy D Browning. “Sums of Arithmetic Functions over Values of Binary Forms.” *Acta Arithmetica* 125, no. 3 (2006): 291–304. https://doi.org/10.4064/aa125-3-6."},"publication":"Acta Arithmetica","abstract":[{"lang":"eng","text":"This paper is concerned with the average order of certain arithmetic functions, as they range over the values taken by binary forms."}],"quality_controlled":0,"doi":"10.4064/aa125-3-6","publisher":"Instytut Matematyczny","date_published":"2006-01-01T00:00:00Z","title":"Sums of arithmetic functions over values of binary forms","month":"01"},{"extern":1,"alternative_title":["Contemporary Mathematics"],"_id":"2333","date_updated":"2020-07-14T12:45:39Z","author":[{"full_name":"Lieb, Élliott H","first_name":"Élliott","last_name":"Lieb"},{"orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","last_name":"Seiringer"},{"last_name":"Solovej","first_name":"Jan","full_name":"Solovej, Jan P"}],"type":"conference","intvolume":" 412","main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0507049","open_access":"1"}],"page":"239 - 248","year":"2006","day":"01","date_created":"2018-12-11T11:57:03Z","oa":1,"publist_id":"4593","conference":{"name":"Differential Equations and Mathematical Physics"},"volume":412,"publication_status":"published","publisher":"American Mathematical Society","month":"01","title":"Ground-state energy of a dilute Fermi gas","date_published":"2006-01-01T00:00:00Z","citation":{"chicago":"Lieb, Élliott, Robert Seiringer, and Jan Solovej. “Ground-State Energy of a Dilute Fermi Gas,” 412:239–48. American Mathematical Society, 2006. https://doi.org/10.1090/conm/412.","mla":"Lieb, Élliott, et al. *Ground-State Energy of a Dilute Fermi Gas*. Vol. 412, American Mathematical Society, 2006, pp. 239–48, doi:10.1090/conm/412.","short":"É. Lieb, R. Seiringer, J. Solovej, in:, American Mathematical Society, 2006, pp. 239–248.","ista":"Lieb É, Seiringer R, Solovej J. 2006. Ground-state energy of a dilute Fermi gas. Differential Equations and Mathematical Physics, Contemporary Mathematics, vol. 412. 239–248.","ieee":"É. Lieb, R. Seiringer, and J. Solovej, “Ground-state energy of a dilute Fermi gas,” presented at the Differential Equations and Mathematical Physics, 2006, vol. 412, pp. 239–248.","ama":"Lieb É, Seiringer R, Solovej J. Ground-state energy of a dilute Fermi gas. In: Vol 412. American Mathematical Society; 2006:239-248. doi:10.1090/conm/412","apa":"Lieb, É., Seiringer, R., & Solovej, J. (2006). Ground-state energy of a dilute Fermi gas (Vol. 412, pp. 239–248). Presented at the Differential Equations and Mathematical Physics, American Mathematical Society. https://doi.org/10.1090/conm/412"},"status":"public","quality_controlled":0,"doi":"10.1090/conm/412"},{"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0305025"}],"date_updated":"2020-07-14T12:45:39Z","_id":"2334","author":[{"full_name":"Robert Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","last_name":"Seiringer","first_name":"Robert"},{"first_name":"Élliott","last_name":"Lieb","full_name":"Lieb, Élliott H"},{"full_name":"Yngvason, Jakob","first_name":"Jakob","last_name":"Yngvason"}],"type":"conference","extern":1,"publist_id":"4592","conference":{"name":"ICMP: International Congress on Mathematical Physics"},"oa":1,"date_created":"2018-12-11T11:57:03Z","day":"07","year":"2006","publication_status":"published","editor":[{"first_name":"Jean","last_name":"Zambrini","full_name":"Zambrini, Jean-Claude"}],"doi":"10.1007/s00220-003-0993-3","quality_controlled":0,"status":"public","citation":{"chicago":"Seiringer, Robert, Élliott Lieb, and Jakob Yngvason. “One-Dimensional Behavior of Dilute, Trapped Bose Gases in Traps.” edited by Jean Zambrini. World Scientific Publishing, 2006. https://doi.org/10.1007/s00220-003-0993-3.","ieee":"R. Seiringer, É. Lieb, and J. Yngvason, “One-dimensional behavior of dilute, trapped Bose gases in traps,” presented at the ICMP: International Congress on Mathematical Physics, 2006.","short":"R. Seiringer, É. Lieb, J. Yngvason, in:, J. Zambrini (Ed.), World Scientific Publishing, 2006.","ista":"Seiringer R, Lieb É, Yngvason J. 2006. One-dimensional behavior of dilute, trapped Bose gases in traps. ICMP: International Congress on Mathematical Physics","mla":"Seiringer, Robert, et al. *One-Dimensional Behavior of Dilute, Trapped Bose Gases in Traps*. Edited by Jean Zambrini, World Scientific Publishing, 2006, doi:10.1007/s00220-003-0993-3.","apa":"Seiringer, R., Lieb, É., & Yngvason, J. (2006). One-dimensional behavior of dilute, trapped Bose gases in traps. In J. Zambrini (Ed.). Presented at the ICMP: International Congress on Mathematical Physics, World Scientific Publishing. https://doi.org/10.1007/s00220-003-0993-3","ama":"Seiringer R, Lieb É, Yngvason J. One-dimensional behavior of dilute, trapped Bose gases in traps. In: Zambrini J, ed. World Scientific Publishing; 2006. doi:10.1007/s00220-003-0993-3"},"date_published":"2006-03-07T00:00:00Z","title":"One-dimensional behavior of dilute, trapped Bose gases in traps","month":"03","publisher":"World Scientific Publishing"},{"author":[{"last_name":"Lieb","first_name":"Élliott","full_name":"Lieb, Élliott H"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Robert Seiringer","orcid":"0000-0002-6781-0521","last_name":"Seiringer","first_name":"Robert"}],"_id":"2363","date_updated":"2020-07-14T12:45:40Z","type":"review","extern":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0504042"}],"intvolume":" 264","year":"2006","page":"505 - 537","day":"01","date_created":"2018-12-11T11:57:13Z","issue":"2","oa":1,"publist_id":"4561","volume":264,"publication_status":"published","publisher":"Springer","date_published":"2006-01-01T00:00:00Z","month":"01","title":"Derivation of the Gross-Pitaevskii equation for rotating Bose gases","status":"public","publication":"Communications in Mathematical Physics","citation":{"apa":"Lieb, É., & Seiringer, R. (2006). Derivation of the Gross-Pitaevskii equation for rotating Bose gases. *Communications in Mathematical Physics*. Springer. https://doi.org/10.1007/s00220-006-1524-9","ama":"Lieb É, Seiringer R. Derivation of the Gross-Pitaevskii equation for rotating Bose gases. *Communications in Mathematical Physics*. 2006;264(2):505-537. doi:10.1007/s00220-006-1524-9","chicago":"Lieb, Élliott, and Robert Seiringer. “Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases.” *Communications in Mathematical Physics*. Springer, 2006. https://doi.org/10.1007/s00220-006-1524-9.","ieee":"É. Lieb and R. Seiringer, “Derivation of the Gross-Pitaevskii equation for rotating Bose gases,” *Communications in Mathematical Physics*, vol. 264, no. 2. Springer, pp. 505–537, 2006.","ista":"Lieb É, Seiringer R. 2006. Derivation of the Gross-Pitaevskii equation for rotating Bose gases. Communications in Mathematical Physics. 264(2), 505–537.","short":"É. Lieb, R. Seiringer, Communications in Mathematical Physics 264 (2006) 505–537.","mla":"Lieb, Élliott, and Robert Seiringer. “Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases.” *Communications in Mathematical Physics*, vol. 264, no. 2, Springer, 2006, pp. 505–37, doi:10.1007/s00220-006-1524-9."},"abstract":[{"text":" We prove that the Gross-Pitaevskii equation correctly describes the ground state energy and corresponding one-particle density matrix of rotating, dilute, trapped Bose gases with repulsive two-body interactions. We also show that there is 100% Bose-Einstein condensation. While a proof that the GP equation correctly describes non-rotating or slowly rotating gases was known for some time, the rapidly rotating case was unclear because the Bose (i.e., symmetric) ground state is not the lowest eigenstate of the Hamiltonian in this case. We have been able to overcome this difficulty with the aid of coherent states. Our proof also conceptually simplifies the previous proof for the slowly rotating case. In the case of axially symmetric traps, our results show that the appearance of quantized vortices causes spontaneous symmetry breaking in the ground state. ","lang":"eng"}],"doi":"10.1007/s00220-006-1524-9","quality_controlled":0}]