---
_id: '18179'
abstract:
- lang: eng
  text: 'Linnik type problems concern the distribution of projections of integral
    points on the unit sphere as their norm increases, and different generalizations
    of this phenomenon. Our work addresses a question of this type: we prove the uniform
    distribution of the projections of primitive Z2 points in the p-adic unit sphere,
    as their (real) norm tends to infinity. The proof is via counting lattice points
    in semi-simple S-arithmetic groups.'
- lang: fre
  text: 'Les problèmes de type Linnik concernent la distribution des projections des
    points entiers sur la sphère unitaire lorsque leur norme augmente et différentes
    généralisations de ce phénomène. Notre travail s’intéresse à une question de ce
    type : nous prouvons la distribution uniforme des projections des points primitifs
    de Z2 sur la sphère unitaire p-adique lorsque leur norme (réelle) tend vers l’infini.
    La preuve se fait en comptant les points d’un réseau dans des S-groupes arithmétiques
    semi-simples.'
acknowledgement: The second author is supported by EPRSC grant EP/P026710/1.
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Antonin
  full_name: Guilloux, Antonin
  last_name: Guilloux
- first_name: Tal
  full_name: Horesh, Tal
  id: C8B7BF48-8D81-11E9-BCA9-F536E6697425
  last_name: Horesh
citation:
  ama: Guilloux A, Horesh T. p-adic directions of primitive vectors. <i>Publications
    mathématiques de Besançon - Algèbre et Théorie des nombres</i>. 2023;2023:85-107.
    doi:<a href="https://doi.org/10.5802/pmb.50">10.5802/pmb.50</a>
  apa: Guilloux, A., &#38; Horesh, T. (2023). p-adic directions of primitive vectors.
    <i>Publications Mathématiques de Besançon - Algèbre et Théorie Des Nombres</i>.
    Presses Universitaires de Franche-Comté. <a href="https://doi.org/10.5802/pmb.50">https://doi.org/10.5802/pmb.50</a>
  chicago: Guilloux, Antonin, and Tal Horesh. “P-Adic Directions of Primitive Vectors.”
    <i>Publications Mathématiques de Besançon - Algèbre et Théorie Des Nombres</i>.
    Presses Universitaires de Franche-Comté, 2023. <a href="https://doi.org/10.5802/pmb.50">https://doi.org/10.5802/pmb.50</a>.
  ieee: A. Guilloux and T. Horesh, “p-adic directions of primitive vectors,” <i>Publications
    mathématiques de Besançon - Algèbre et Théorie des nombres</i>, vol. 2023. Presses
    Universitaires de Franche-Comté, pp. 85–107, 2023.
  ista: Guilloux A, Horesh T. 2023. p-adic directions of primitive vectors. Publications
    mathématiques de Besançon - Algèbre et Théorie des nombres. 2023, 85–107.
  mla: Guilloux, Antonin, and Tal Horesh. “P-Adic Directions of Primitive Vectors.”
    <i>Publications Mathématiques de Besançon - Algèbre et Théorie Des Nombres</i>,
    vol. 2023, Presses Universitaires de Franche-Comté, 2023, pp. 85–107, doi:<a href="https://doi.org/10.5802/pmb.50">10.5802/pmb.50</a>.
  short: A. Guilloux, T. Horesh, Publications Mathématiques de Besançon - Algèbre
    et Théorie Des Nombres 2023 (2023) 85–107.
corr_author: '1'
date_created: 2024-10-06T22:01:13Z
date_published: 2023-06-15T00:00:00Z
date_updated: 2025-04-14T09:25:44Z
day: '15'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.5802/pmb.50
external_id:
  arxiv:
  - '2103.10889'
file:
- access_level: open_access
  checksum: cefc47a2cf55a87f8e4960197f73353b
  content_type: application/pdf
  creator: dernst
  date_created: 2024-10-07T11:32:32Z
  date_updated: 2024-10-07T11:32:32Z
  file_id: '18186'
  file_name: 2023_MathBesancon_Guilloux.pdf
  file_size: 1399390
  relation: main_file
  success: 1
file_date_updated: 2024-10-07T11:32:32Z
has_accepted_license: '1'
intvolume: '      2023'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nd/4.0/
month: '06'
oa: 1
oa_version: Published Version
page: 85-107
project:
- _id: 26A8D266-B435-11E9-9278-68D0E5697425
  grant_number: EP-P026710-2
  name: Between rational and integral points
publication: Publications mathématiques de Besançon - Algèbre et Théorie des nombres
publication_identifier:
  eissn:
  - 2592-6616
  issn:
  - 2804-8504
publication_status: published
publisher: Presses Universitaires de Franche-Comté
quality_controlled: '1'
scopus_import: '1'
status: public
title: p-adic directions of primitive vectors
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: 2023
year: '2023'
...