{"author":[{"orcid":"0000-0002-8314-0177","full_name":"Timothy Browning","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D"},{"last_name":"Heath Brown","full_name":"Heath-Brown, Roger","first_name":"Roger"},{"full_name":"Starr, Jason M","last_name":"Starr","first_name":"Jason"}],"date_published":"2006-09-01T00:00:00Z","year":"2006","type":"journal_article","day":"01","status":"public","publication":"Proceedings of the London Mathematical Society","date_created":"2018-12-11T11:45:14Z","month":"09","date_updated":"2021-01-12T06:55:29Z","page":"273 - 303","volume":93,"title":"The density of rational points on non-singular hypersurfaces, II","_id":"213","quality_controlled":0,"intvolume":"        93","abstract":[{"text":"For any integers d,n ≥2, let X ⊂ Pn be a non‐singular hypersurface of degree d that is defined over the rational numbers. The main result in this paper is a proof that the number of rational points on X which have height at most B is O(Bn − 1 + ɛ), for any ɛ &gt; 0. The implied constant in this estimate depends at most upon d, ɛ and n. 2000 Mathematics Subject Classification 11D45 (primary), 11G35, 14G05 (secondary).","lang":"eng"}],"publist_id":"7698","publisher":"John Wiley and Sons Ltd","extern":1,"issue":"2","publication_status":"published","citation":{"ieee":"T. D. Browning, R. Heath Brown, and J. Starr, “The density of rational points on non-singular hypersurfaces, II,” <i>Proceedings of the London Mathematical Society</i>, vol. 93, no. 2. John Wiley and Sons Ltd, pp. 273–303, 2006.","ama":"Browning TD, Heath Brown R, Starr J. The density of rational points on non-singular hypersurfaces, II. <i>Proceedings of the London Mathematical Society</i>. 2006;93(2):273-303. doi:<a href=\"https://doi.org/10.1112/S0024611506015784\">https://doi.org/10.1112/S0024611506015784</a>","chicago":"Browning, Timothy D, Roger Heath Brown, and Jason Starr. “The Density of Rational Points on Non-Singular Hypersurfaces, II.” <i>Proceedings of the London Mathematical Society</i>. John Wiley and Sons Ltd, 2006. <a href=\"https://doi.org/10.1112/S0024611506015784\">https://doi.org/10.1112/S0024611506015784</a>.","mla":"Browning, Timothy D., et al. “The Density of Rational Points on Non-Singular Hypersurfaces, II.” <i>Proceedings of the London Mathematical Society</i>, vol. 93, no. 2, John Wiley and Sons Ltd, 2006, pp. 273–303, doi:<a href=\"https://doi.org/10.1112/S0024611506015784\">https://doi.org/10.1112/S0024611506015784</a>.","ista":"Browning TD, Heath Brown R, Starr J. 2006. The density of rational points on non-singular hypersurfaces, II. Proceedings of the London Mathematical Society. 93(2), 273–303.","short":"T.D. Browning, R. Heath Brown, J. Starr, Proceedings of the London Mathematical Society 93 (2006) 273–303.","apa":"Browning, T. D., Heath Brown, R., &#38; Starr, J. (2006). The density of rational points on non-singular hypersurfaces, II. <i>Proceedings of the London Mathematical Society</i>. John Wiley and Sons Ltd. <a href=\"https://doi.org/10.1112/S0024611506015784\">https://doi.org/10.1112/S0024611506015784</a>"},"doi":"https://doi.org/10.1112/S0024611506015784","acknowledgement":"EPSRC grant number GR/R93155/01"}