---
OA_place: publisher
OA_type: hybrid
_id: '20850'
abstract:
- lang: eng
  text: We provide an estimate for the number of nontrivial integer points on the
    Pellian surface t^2 - du^2 = 1 in a bounded region. We give a lower bound on the
    size of fundamental solutions for almost all d in a certain class, based on a
    recent conjecture of Browning and Wilsch about integer points on log K3 surfaces.
    We also obtain an upper bound on the average of class number in this class, assuming
    the same conjecture.
- lang: fre
  text: "Nous donnons une estimation du nombre de points entiers non triviaux sur
    la surface pellienne \r\nt^2 - du^2 = 1 dans une région bornée. Nous établissons
    une borne inférieure pour la taille des solutions fondamentales pour presque tout
    d appartenant à une certaine classe, en nous fondant sur une conjecture récente
    de Browning et Wilsch concernant les points entiers sur les surfaces log K3. Nous
    obtenons également une borne supérieure pour la moyenne du nombre de classes dans
    cette classe, sous la même hypothèse conjecturale."
acknowledgement: The author would like to thank his supervisor Tim Browning for suggesting
  this project and many helpful conversations and useful comments. Moreover, he is
  grateful to Jakob Glas, Damaris Schindler, Igor Shparlinski, Matteo Verzobio, Victor
  Wang, Florian Wilsch and Shuntaro Yamagishi for taking their time to answer his
  questions and their valuable suggestions.
article_processing_charge: Yes (in subscription journal)
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. Class numbers and integer points on some Pellian surfaces. <i>Journal
    de theorie des nombres de Bordeaux</i>. 2025;37(3):973-988. doi:<a href="https://doi.org/10.5802/jtnb.1348">10.5802/jtnb.1348</a>
  apa: Diao, Y. (2025). Class numbers and integer points on some Pellian surfaces.
    <i>Journal de Theorie Des Nombres de Bordeaux</i>. Université de Bordeaux. <a
    href="https://doi.org/10.5802/jtnb.1348">https://doi.org/10.5802/jtnb.1348</a>
  chicago: Diao, Yijie. “Class Numbers and Integer Points on Some Pellian Surfaces.”
    <i>Journal de Theorie Des Nombres de Bordeaux</i>. Université de Bordeaux, 2025.
    <a href="https://doi.org/10.5802/jtnb.1348">https://doi.org/10.5802/jtnb.1348</a>.
  ieee: Y. Diao, “Class numbers and integer points on some Pellian surfaces,” <i>Journal
    de theorie des nombres de Bordeaux</i>, vol. 37, no. 3. Université de Bordeaux,
    pp. 973–988, 2025.
  ista: Diao Y. 2025. Class numbers and integer points on some Pellian surfaces. Journal
    de theorie des nombres de Bordeaux. 37(3), 973–988.
  mla: Diao, Yijie. “Class Numbers and Integer Points on Some Pellian Surfaces.” <i>Journal
    de Theorie Des Nombres de Bordeaux</i>, vol. 37, no. 3, Université de Bordeaux,
    2025, pp. 973–88, doi:<a href="https://doi.org/10.5802/jtnb.1348">10.5802/jtnb.1348</a>.
  short: Y. Diao, Journal de Theorie Des Nombres de Bordeaux 37 (2025) 973–988.
corr_author: '1'
date_created: 2025-12-21T23:01:35Z
date_published: 2025-11-27T00:00:00Z
date_updated: 2025-12-29T10:08:46Z
day: '27'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.5802/jtnb.1348
external_id:
  arxiv:
  - '2408.03774'
file:
- access_level: open_access
  checksum: 67aa0afbc0b5bcbff5341f4d25e6ba20
  content_type: application/pdf
  creator: dernst
  date_created: 2025-12-29T10:05:22Z
  date_updated: 2025-12-29T10:05:22Z
  file_id: '20861'
  file_name: 2025_JTNB_Diao.pdf
  file_size: 766196
  relation: main_file
  success: 1
file_date_updated: 2025-12-29T10:05:22Z
has_accepted_license: '1'
intvolume: '        37'
issue: '3'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nd/4.0/
month: '11'
oa: 1
oa_version: Published Version
page: 973-988
publication: Journal de theorie des nombres de Bordeaux
publication_identifier:
  eissn:
  - 2118-8572
  issn:
  - 1246-7405
publication_status: published
publisher: Université de Bordeaux
quality_controlled: '1'
scopus_import: '1'
status: public
title: Class numbers and integer points on some Pellian surfaces
tmp:
  image: /image/cc_by_nd.png
  legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode
  name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)
  short: CC BY-ND (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 37
year: '2025'
...
---
_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.
corr_author: '1'
date_created: 2023-01-26T21:17:04Z
date_published: 2023-01-09T00:00:00Z
date_updated: 2024-10-21T06:01:30Z
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'
scopus_import: '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'
...