---
_id: '12776'
abstract:
- lang: eng
  text: An improved asymptotic formula is established for the number of rational points
    of bounded height on the split smooth del Pezzo surface of degree 5. The proof
    uses the five conic bundle structures on the surface.
acknowledgement: This work was begun while the author was participating in the programme
  on "Diophantine equations" at the Hausdorff Research Institute for Mathematics in
  Bonn in 2009. The hospitality and financial support of the institute is gratefully
  acknowledged. The idea of using conic bundles to study the split del Pezzo surface
  of degree 5 was explained to the author by Professor Salberger. The author is very
  grateful to him for his input into this project and also to Shuntaro Yamagishi for
  many useful comments on an earlier version of this manuscript. While working on
  this paper the author was supported by FWF grant P32428-N35.
article_processing_charge: No
article_type: original
author:
- first_name: Timothy D
  full_name: Browning, Timothy D
  id: 35827D50-F248-11E8-B48F-1D18A9856A87
  last_name: Browning
  orcid: 0000-0002-8314-0177
citation:
  ama: Browning TD. Revisiting the Manin–Peyre conjecture for the split del Pezzo
    surface of degree 5. <i>New York Journal of Mathematics</i>. 2022;28:1193-1229.
  apa: Browning, T. D. (2022). Revisiting the Manin–Peyre conjecture for the split
    del Pezzo surface of degree 5. <i>New York Journal of Mathematics</i>. State University
    of New York.
  chicago: Browning, Timothy D. “Revisiting the Manin–Peyre Conjecture for the Split
    Del Pezzo Surface of Degree 5.” <i>New York Journal of Mathematics</i>. State
    University of New York, 2022.
  ieee: T. D. Browning, “Revisiting the Manin–Peyre conjecture for the split del Pezzo
    surface of degree 5,” <i>New York Journal of Mathematics</i>, vol. 28. State University
    of New York, pp. 1193–1229, 2022.
  ista: Browning TD. 2022. Revisiting the Manin–Peyre conjecture for the split del
    Pezzo surface of degree 5. New York Journal of Mathematics. 28, 1193–1229.
  mla: Browning, Timothy D. “Revisiting the Manin–Peyre Conjecture for the Split Del
    Pezzo Surface of Degree 5.” <i>New York Journal of Mathematics</i>, vol. 28, State
    University of New York, 2022, pp. 1193–229.
  short: T.D. Browning, New York Journal of Mathematics 28 (2022) 1193–1229.
date_created: 2023-03-28T09:21:09Z
date_published: 2022-08-24T00:00:00Z
date_updated: 2023-10-18T07:59:13Z
day: '24'
ddc:
- '510'
department:
- _id: TiBr
file:
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  creator: dernst
  date_created: 2023-03-30T07:09:35Z
  date_updated: 2023-03-30T07:09:35Z
  file_id: '12778'
  file_name: 2022_NYJM_Browning.pdf
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has_accepted_license: '1'
intvolume: '        28'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 1193 - 1229
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P32428
  name: New frontiers of the Manin conjecture
publication: New York Journal of Mathematics
publication_identifier:
  issn:
  - 1076-9803
publication_status: published
publisher: State University of New York
quality_controlled: '1'
status: public
title: Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree
  5
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2022'
...