---
_id: '178'
abstract:
- lang: eng
  text: We give an upper bound for the number of rational points of height at most
    B, lying on a surface defined by a quadratic form Q. The bound shows an explicit
    dependence on Q. It is optimal with respect to B, and is also optimal for typical
    forms Q.
article_processing_charge: No
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 quadric surfaces. <i>Discrete
    Analysis</i>. 2018;15:1-29. doi:<a href="https://doi.org/10.19086/da.4375">10.19086/da.4375</a>
  apa: Browning, T. D., &#38; Heath-Brown, R. (2018). Counting rational points on
    quadric surfaces. <i>Discrete Analysis</i>. Alliance of Diamond Open Access Journals.
    <a href="https://doi.org/10.19086/da.4375">https://doi.org/10.19086/da.4375</a>
  chicago: Browning, Timothy D, and Roger Heath-Brown. “Counting Rational Points on
    Quadric Surfaces.” <i>Discrete Analysis</i>. Alliance of Diamond Open Access Journals,
    2018. <a href="https://doi.org/10.19086/da.4375">https://doi.org/10.19086/da.4375</a>.
  ieee: T. D. Browning and R. Heath-Brown, “Counting rational points on quadric surfaces,”
    <i>Discrete Analysis</i>, vol. 15. Alliance of Diamond Open Access Journals, pp.
    1–29, 2018.
  ista: Browning TD, Heath-Brown R. 2018. Counting rational points on quadric surfaces.
    Discrete Analysis. 15, 1–29.
  mla: Browning, Timothy D., and Roger Heath-Brown. “Counting Rational Points on Quadric
    Surfaces.” <i>Discrete Analysis</i>, vol. 15, Alliance of Diamond Open Access
    Journals, 2018, pp. 1–29, doi:<a href="https://doi.org/10.19086/da.4375">10.19086/da.4375</a>.
  short: T.D. Browning, R. Heath-Brown, Discrete Analysis 15 (2018) 1–29.
date_created: 2018-12-11T11:45:02Z
date_published: 2018-09-07T00:00:00Z
date_updated: 2022-08-26T09:13:02Z
day: '07'
ddc:
- '512'
doi: 10.19086/da.4375
extern: '1'
external_id:
  arxiv:
  - '1801.00979'
intvolume: '        15'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1801.00979
month: '09'
oa: 1
oa_version: Preprint
page: 1 - 29
publication: Discrete Analysis
publication_identifier:
  eissn:
  - 2397-3129
publication_status: published
publisher: Alliance of Diamond Open Access Journals
quality_controlled: '1'
status: public
title: Counting rational points on quadric surfaces
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 15
year: '2018'
...