[{"type":"journal_article","month":"01","status":"public","title":"The geometric sieve for quadrics","publisher":"De Gruyter","_id":"8742","isi":1,"department":[{"_id":"TiBr"}],"quality_controlled":"1","issue":"1","article_type":"original","date_updated":"2025-04-15T07:39:01Z","citation":{"apa":"Browning, T. D., &#38; Heath-Brown, R. (2021). The geometric sieve for quadrics. <i>Forum Mathematicum</i>. De Gruyter. <a href=\"https://doi.org/10.1515/forum-2020-0074\">https://doi.org/10.1515/forum-2020-0074</a>","ieee":"T. D. Browning and R. Heath-Brown, “The geometric sieve for quadrics,” <i>Forum Mathematicum</i>, vol. 33, no. 1. De Gruyter, pp. 147–165, 2021.","short":"T.D. Browning, R. Heath-Brown, Forum Mathematicum 33 (2021) 147–165.","ista":"Browning TD, Heath-Brown R. 2021. The geometric sieve for quadrics. Forum Mathematicum. 33(1), 147–165.","chicago":"Browning, Timothy D, and Roger Heath-Brown. “The Geometric Sieve for Quadrics.” <i>Forum Mathematicum</i>. De Gruyter, 2021. <a href=\"https://doi.org/10.1515/forum-2020-0074\">https://doi.org/10.1515/forum-2020-0074</a>.","mla":"Browning, Timothy D., and Roger Heath-Brown. “The Geometric Sieve for Quadrics.” <i>Forum Mathematicum</i>, vol. 33, no. 1, De Gruyter, 2021, pp. 147–65, doi:<a href=\"https://doi.org/10.1515/forum-2020-0074\">10.1515/forum-2020-0074</a>.","ama":"Browning TD, Heath-Brown R. The geometric sieve for quadrics. <i>Forum Mathematicum</i>. 2021;33(1):147-165. doi:<a href=\"https://doi.org/10.1515/forum-2020-0074\">10.1515/forum-2020-0074</a>"},"page":"147-165","date_created":"2020-11-08T23:01:25Z","main_file_link":[{"url":"https://arxiv.org/abs/2003.09593","open_access":"1"}],"project":[{"_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","name":"New frontiers of the Manin conjecture","call_identifier":"FWF","grant_number":"P32428"}],"oa_version":"Preprint","volume":33,"intvolume":"        33","arxiv":1,"year":"2021","abstract":[{"text":"We develop a version of Ekedahl’s geometric sieve for integral quadratic forms of rank at least five. As one ranges over the zeros of such quadratic forms, we use the sieve to compute the density of coprime values of polynomials, and furthermore, to address a question about local solubility in families of varieties parameterised by the zeros.","lang":"eng"}],"doi":"10.1515/forum-2020-0074","date_published":"2021-01-01T00:00:00Z","article_processing_charge":"No","publication":"Forum Mathematicum","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"day":"01","publication_identifier":{"issn":["0933-7741"],"eissn":["1435-5337"]},"oa":1,"author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","last_name":"Browning","full_name":"Browning, Timothy D","first_name":"Timothy D"},{"last_name":"Heath-Brown","first_name":"Roger","full_name":"Heath-Brown, Roger"}],"scopus_import":"1","external_id":{"arxiv":["2003.09593"],"isi":["000604750900008"]},"publication_status":"published"},{"quality_controlled":"1","_id":"257","publisher":"De Gruyter","status":"public","title":"Pairs of diagonal quadratic forms and linear correlations among sums of two squares","type":"journal_article","month":"07","extern":"1","page":"2025 - 2050","citation":{"chicago":"Browning, Timothy D, and Ritabrata Munshi. “Pairs of Diagonal Quadratic Forms and Linear Correlations among Sums of Two Squares.” <i>Forum Mathematicum</i>. De Gruyter, 2015. <a href=\"https://doi.org/10.1515/forum-2013-6024\">https://doi.org/10.1515/forum-2013-6024</a>.","mla":"Browning, Timothy D., and Ritabrata Munshi. “Pairs of Diagonal Quadratic Forms and Linear Correlations among Sums of Two Squares.” <i>Forum Mathematicum</i>, vol. 27, no. 4, De Gruyter, 2015, pp. 2025–50, doi:<a href=\"https://doi.org/10.1515/forum-2013-6024\">10.1515/forum-2013-6024</a>.","ama":"Browning TD, Munshi R. Pairs of diagonal quadratic forms and linear correlations among sums of two squares. <i>Forum Mathematicum</i>. 2015;27(4):2025-2050. doi:<a href=\"https://doi.org/10.1515/forum-2013-6024\">10.1515/forum-2013-6024</a>","apa":"Browning, T. D., &#38; Munshi, R. (2015). Pairs of diagonal quadratic forms and linear correlations among sums of two squares. <i>Forum Mathematicum</i>. De Gruyter. <a href=\"https://doi.org/10.1515/forum-2013-6024\">https://doi.org/10.1515/forum-2013-6024</a>","ieee":"T. D. Browning and R. Munshi, “Pairs of diagonal quadratic forms and linear correlations among sums of two squares,” <i>Forum Mathematicum</i>, vol. 27, no. 4. De Gruyter, pp. 2025–2050, 2015.","short":"T.D. Browning, R. Munshi, Forum Mathematicum 27 (2015) 2025–2050.","ista":"Browning TD, Munshi R. 2015. Pairs of diagonal quadratic forms and linear correlations among sums of two squares. Forum Mathematicum. 27(4), 2025–2050."},"date_updated":"2026-05-19T13:08:06Z","article_type":"original","issue":"4","publication":"Forum Mathematicum","date_published":"2015-07-10T00:00:00Z","article_processing_charge":"No","doi":"10.1515/forum-2013-6024","abstract":[{"lang":"eng","text":"For suitable pairs of diagonal quadratic forms in eight variables we use the circle method to investigate the density of simultaneous integer solutions and relate this to the problem of estimating linear correlations among sums of two squares."}],"year":"2015","arxiv":1,"intvolume":"        27","acknowledgement":"While working on this paper the first author was supported by ERC grant 306457 and the second author was supported by SwarnaJayanti Fellowship 2011–12, DST, Government of India.","volume":27,"oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1302.2434","open_access":"1"}],"date_created":"2018-12-11T11:45:28Z","publist_id":"7645","publication_status":"published","OA_type":"green","scopus_import":"1","external_id":{"arxiv":["1302.2434"]},"author":[{"orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","first_name":"Timothy D","last_name":"Browning"},{"first_name":"Ritabrata","full_name":"Munshi, Ritabrata","last_name":"Munshi"}],"oa":1,"OA_place":"repository","publication_identifier":{"issn":["0933-7741"],"eissn":["1435-5337"]},"language":[{"iso":"eng"}],"day":"10","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd"},{"year":"2008","arxiv":1,"intvolume":"        20","doi":"10.1515/forum.2008.042","publication":"Forum Mathematicum","date_published":"2008-11-03T00:00:00Z","article_processing_charge":"No","abstract":[{"text":"We consider the minimal mass m0 required for solutions to the mass-critical nonlinear Schrödinger (NLS) equation iut + Δu = μ|u|^4/d u to blow up. If m0 is finite, we show that there exists a minimal-mass solution blowing up (in the sense of an infinite spacetime norm) in both time directions, whose orbit in  is compact after quotienting out by the symmetries of the equation. A similar result is obtained for spherically symmetric solutions. Similar results were previously obtained by Keraani, [Keraani S.: On the blow-up phenomenon of the critical nonlinear Schrödinger equation. J. Funct. Anal. 235 (2006), 171–192], in dimensions 1, 2 and Begout and Vargas, [Begout P., Vargas A.: Mass concentration phenomena for the L2-critical nonlinear Schrödinger equation, preprint], in dimensions d ≥ 3 for the mass-critical NLS and by Kenig and Merle, [Kenig C., Merle F.: Global well-posedness, scattering, and blowup for the energy-critical, focusing, non-linear Schrödinger equation in the radial case, preprint], in the energy-critical case. In a subsequent paper we shall use this compactness result to establish global existence and scattering in  for the defocusing NLS in three and higher dimensions with spherically symmetric data.","lang":"eng"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.math/0609690","open_access":"1"}],"date_created":"2026-06-19T07:53:12Z","oa_version":"Preprint","volume":20,"publication_status":"published","OA_type":"green","das_tickbox":"1","author":[{"last_name":"Tao","full_name":"Tao, Terence","first_name":"Terence"},{"id":"056daca0-b8d1-11f0-964f-f91054abf8ca","last_name":"Visan","first_name":"Monica","full_name":"Visan, Monica"},{"last_name":"Zhang","full_name":"Zhang, Xiaoyi","first_name":"Xiaoyi"}],"mathsc":["35Q55"],"scopus_import":"1","external_id":{"arxiv":["math/0609690"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"day":"03","publication_identifier":{"eissn":["1435-5337"],"issn":["0933-7741"]},"OA_place":"repository","oa":1,"quality_controlled":"1","publisher":"De Gruyter","type":"journal_article","month":"11","status":"public","title":"Minimal-mass blowup solutions of the mass-critical NLS","_id":"22049","citation":{"apa":"Tao, T., Vişan, M., &#38; Zhang, X. (2008). Minimal-mass blowup solutions of the mass-critical NLS. <i>Forum Mathematicum</i>. De Gruyter. <a href=\"https://doi.org/10.1515/forum.2008.042\">https://doi.org/10.1515/forum.2008.042</a>","ieee":"T. Tao, M. Vişan, and X. Zhang, “Minimal-mass blowup solutions of the mass-critical NLS,” <i>Forum Mathematicum</i>, vol. 20, no. 5. De Gruyter, pp. 881–919, 2008.","short":"T. Tao, M. Vişan, X. Zhang, Forum Mathematicum 20 (2008) 881–919.","ista":"Tao T, Vişan M, Zhang X. 2008. Minimal-mass blowup solutions of the mass-critical NLS. Forum Mathematicum. 20(5), 881–919.","chicago":"Tao, Terence, Monica Vişan, and Xiaoyi Zhang. “Minimal-Mass Blowup Solutions of the Mass-Critical NLS.” <i>Forum Mathematicum</i>. De Gruyter, 2008. <a href=\"https://doi.org/10.1515/forum.2008.042\">https://doi.org/10.1515/forum.2008.042</a>.","ama":"Tao T, Vişan M, Zhang X. Minimal-mass blowup solutions of the mass-critical NLS. <i>Forum Mathematicum</i>. 2008;20(5):881-919. doi:<a href=\"https://doi.org/10.1515/forum.2008.042\">10.1515/forum.2008.042</a>","mla":"Tao, Terence, et al. “Minimal-Mass Blowup Solutions of the Mass-Critical NLS.” <i>Forum Mathematicum</i>, vol. 20, no. 5, De Gruyter, 2008, pp. 881–919, doi:<a href=\"https://doi.org/10.1515/forum.2008.042\">10.1515/forum.2008.042</a>."},"date_updated":"2026-06-25T08:15:22Z","extern":"1","page":"881-919","article_type":"original","issue":"5"}]