---
_id: '12406'
abstract:
- lang: eng
  text: Let X be a sufficiently large positive integer. We prove that one may choose
    a subset S of primes with cardinality O(logX) such that a positive proportion
    of integers less than X can be represented by x2+py2 for at least one p∈S.
acknowledgement: "This article is a version the author’s master thesis at the University
  of Bonn. The author would like to thank his advisor Valentin Blomer for introducing
  the problem, and giving generous feedback and encouragement along the way, especially
  during the global pandemic.\r\nThe author thanks Edgar Assing for his lectures on
  analytic number theory. Finally, the author is grateful to the anonymous referees
  for their valuable time and comments.\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Yijie
  full_name: Diao, Yijie
  id: 7b7eb4ca-eb2c-11ec-b98b-accec0b20c3b
  last_name: Diao
  orcid: 0000-0002-4989-5330
citation:
  ama: Diao Y. Density of the union of positive diagonal binary quadratic forms. <i>Acta
    Arithmetica</i>. 2023;207:1-17. doi:<a href="https://doi.org/10.4064/aa210830-24-11">10.4064/aa210830-24-11</a>
  apa: Diao, Y. (2023). Density of the union of positive diagonal binary quadratic
    forms. <i>Acta Arithmetica</i>. Instytut Matematyczny. <a href="https://doi.org/10.4064/aa210830-24-11">https://doi.org/10.4064/aa210830-24-11</a>
  chicago: Diao, Yijie. “Density of the Union of Positive Diagonal Binary Quadratic
    Forms.” <i>Acta Arithmetica</i>. Instytut Matematyczny, 2023. <a href="https://doi.org/10.4064/aa210830-24-11">https://doi.org/10.4064/aa210830-24-11</a>.
  ieee: Y. Diao, “Density of the union of positive diagonal binary quadratic forms,”
    <i>Acta Arithmetica</i>, vol. 207. Instytut Matematyczny, pp. 1–17, 2023.
  ista: Diao Y. 2023. Density of the union of positive diagonal binary quadratic forms.
    Acta Arithmetica. 207, 1–17.
  mla: Diao, Yijie. “Density of the Union of Positive Diagonal Binary Quadratic Forms.”
    <i>Acta Arithmetica</i>, vol. 207, Instytut Matematyczny, 2023, pp. 1–17, doi:<a
    href="https://doi.org/10.4064/aa210830-24-11">10.4064/aa210830-24-11</a>.
  short: Y. Diao, Acta Arithmetica 207 (2023) 1–17.
date_created: 2023-01-26T21:17:04Z
date_published: 2023-01-09T00:00:00Z
date_updated: 2023-10-17T09:15:17Z
day: '09'
department:
- _id: GradSch
doi: 10.4064/aa210830-24-11
external_id:
  arxiv:
  - '2103.08268'
  isi:
  - '000912903000001'
intvolume: '       207'
isi: 1
keyword:
- Algebra
- Number Theory
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2103.08268
month: '01'
oa: 1
oa_version: Preprint
page: 1-17
publication: Acta Arithmetica
publication_identifier:
  eissn:
  - 1730-6264
  issn:
  - 0065-1036
publication_status: published
publisher: Instytut Matematyczny
quality_controlled: '1'
status: public
title: Density of the union of positive diagonal binary quadratic forms
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 207
year: '2023'
...