--- _id: '213' abstract: - lang: eng 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 > 0. The implied constant in this estimate depends at most upon d, ɛ and n. 2000 Mathematics Subject Classification 11D45 (primary), 11G35, 14G05 (secondary). acknowledgement: EPSRC grant number GR/R93155/01 author: - first_name: Timothy D full_name: Timothy Browning id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: Roger full_name: Heath-Brown, Roger last_name: Heath Brown - first_name: Jason full_name: Starr, Jason M last_name: Starr citation: ama: Browning TD, Heath Brown R, Starr J. The density of rational points on non-singular hypersurfaces, II. Proceedings of the London Mathematical Society. 2006;93(2):273-303. doi:https://doi.org/10.1112/S0024611506015784 apa: Browning, T. D., Heath Brown, R., & Starr, J. (2006). The density of rational points on non-singular hypersurfaces, II. Proceedings of the London Mathematical Society. John Wiley and Sons Ltd. https://doi.org/10.1112/S0024611506015784 chicago: Browning, Timothy D, Roger Heath Brown, and Jason Starr. “The Density of Rational Points on Non-Singular Hypersurfaces, II.” Proceedings of the London Mathematical Society. John Wiley and Sons Ltd, 2006. https://doi.org/10.1112/S0024611506015784. ieee: T. D. Browning, R. Heath Brown, and J. Starr, “The density of rational points on non-singular hypersurfaces, II,” Proceedings of the London Mathematical Society, vol. 93, no. 2. John Wiley and Sons Ltd, pp. 273–303, 2006. 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. mla: Browning, Timothy D., et al. “The Density of Rational Points on Non-Singular Hypersurfaces, II.” Proceedings of the London Mathematical Society, vol. 93, no. 2, John Wiley and Sons Ltd, 2006, pp. 273–303, doi:https://doi.org/10.1112/S0024611506015784. short: T.D. Browning, R. Heath Brown, J. Starr, Proceedings of the London Mathematical Society 93 (2006) 273–303. date_created: 2018-12-11T11:45:14Z date_published: 2006-09-01T00:00:00Z date_updated: 2021-01-12T06:55:29Z day: '01' doi: https://doi.org/10.1112/S0024611506015784 extern: 1 intvolume: ' 93' issue: '2' month: '09' page: 273 - 303 publication: Proceedings of the London Mathematical Society publication_status: published publisher: John Wiley and Sons Ltd publist_id: '7698' quality_controlled: 0 status: public title: The density of rational points on non-singular hypersurfaces, II type: journal_article volume: 93 year: '2006' ...