---
OA_place: repository
OA_type: green
_id: '212'
abstract:
- lang: eng
  text: For any n ≧ 2, let F ∈ ℤ [ x 1, … , xn ] be a form of degree d≧ 2, which produces
    a geometrically irreducible hypersurface in ℙn–1. This paper is concerned with
    the number N(F;B) of rational points on F = 0 which have height at most B. For
    any ε > 0 we establish the estimate N(F; B) = O(B n− 2+ ε ), whenever either
    n ≦ 5 or the hypersurface is not a union of lines. Here the implied constant depends
    at most upon d, n and ε.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Timothy D
  full_name: Browning, Timothy D
  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
citation:
  ama: Browning TD, Heath Brown R. Counting rational points on hypersurfaces. <i>Journal
    fur die Reine und Angewandte Mathematik</i>. 2005;(584):83-115. doi:<a href="https://doi.org/10.1515/crll.2005.2005.584.83">https://doi.org/10.1515/crll.2005.2005.584.83</a>
  apa: Browning, T. D., &#38; Heath Brown, R. (2005). Counting rational points on
    hypersurfaces. <i>Journal Fur Die Reine Und Angewandte Mathematik</i>. Walter
    de Gruyter and Co . <a href="https://doi.org/10.1515/crll.2005.2005.584.83">https://doi.org/10.1515/crll.2005.2005.584.83</a>
  chicago: Browning, Timothy D, and Roger Heath Brown. “Counting Rational Points on
    Hypersurfaces.” <i>Journal Fur Die Reine Und Angewandte Mathematik</i>. Walter
    de Gruyter and Co , 2005. <a href="https://doi.org/10.1515/crll.2005.2005.584.83">https://doi.org/10.1515/crll.2005.2005.584.83</a>.
  ieee: T. D. Browning and R. Heath Brown, “Counting rational points on hypersurfaces,”
    <i>Journal fur die Reine und Angewandte Mathematik</i>, no. 584. Walter de Gruyter
    and Co , pp. 83–115, 2005.
  ista: Browning TD, Heath Brown R. 2005. Counting rational points on hypersurfaces.
    Journal fur die Reine und Angewandte Mathematik. (584), 83–115.
  mla: Browning, Timothy D., and Roger Heath Brown. “Counting Rational Points on Hypersurfaces.”
    <i>Journal Fur Die Reine Und Angewandte Mathematik</i>, no. 584, Walter de Gruyter
    and Co , 2005, pp. 83–115, doi:<a href="https://doi.org/10.1515/crll.2005.2005.584.83">https://doi.org/10.1515/crll.2005.2005.584.83</a>.
  short: T.D. Browning, R. Heath Brown, Journal Fur Die Reine Und Angewandte Mathematik
    (2005) 83–115.
date_created: 2018-12-11T11:45:14Z
date_published: 2005-11-26T00:00:00Z
date_updated: 2026-08-21T09:31:08Z
day: '26'
doi: https://doi.org/10.1515/crll.2005.2005.584.83
extern: '1'
external_id:
  arxiv:
  - abs/math/0404456
issue: '584'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/0707.2296
month: '11'
oa: 1
oa_version: None
page: 83 - 115
publication: Journal fur die Reine und Angewandte Mathematik
publication_identifier:
  issn:
  - 0075-4102
publication_status: published
publisher: 'Walter de Gruyter and Co '
publist_id: '7701'
status: public
title: Counting rational points on hypersurfaces
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2005'
...