---
OA_place: repository
OA_type: green
_id: '22821'
abstract:
- lang: eng
  text: "With probability 1, we assess the average behaviour of various arithmetic
    functions at the values of degree \U0001D451 polynomials \U0001D453∈ℤ⁢[\U0001D461]
    that are ordered by height. This allows us to establish averaged versions of the
    Bateman–Horn conjecture, the polynomial Chowla conjecture and to address a basic
    question about the integral Hasse principle for norm form equations. Moreover,
    we are able to quantify the error term in the asymptotics and the size of the
    exceptional set of \U0001D453, both with arbitrary logarithmic power savings."
acknowledgement: Tim Browning was supported by an FWF grant (DOI 10.55776/P32428),
  Efthymios Sofos was supported by EPSRC New Horizons grant EP/V048236/1, and Joni
  Teräväinen was supported by Academy of Finland grant no. 340098, a von Neumann Fellowship
  (NSF grant DMS-1926686), and funding from European Union’s Horizon Europe research
  and innovation programme under Marie Skłodowska-Curie grant agreement no. 101058904.
  This material is based upon work supported by a grant from the Institute for Advanced
  Study School of Mathematics. The authors are extremely grateful to the anonymous
  referee and to Yijie Diao for useful comments.
article_processing_charge: No
article_type: original
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: Efthymios
  full_name: Sofos, Efthymios
  last_name: Sofos
- first_name: Joni
  full_name: Teräväinen, Joni
  last_name: Teräväinen
citation:
  ama: Browning TD, Sofos E, Teräväinen J. Bateman-Horn, polynomial Chowla and the
    Hasse principle with probability. <i>Journal für die reine und angewandte Mathematik</i>.
    2026. doi:<a href="https://doi.org/10.1515/crelle-2026-0062">10.1515/crelle-2026-0062</a>
  apa: Browning, T. D., Sofos, E., &#38; Teräväinen, J. (2026). Bateman-Horn, polynomial
    Chowla and the Hasse principle with probability. <i>Journal Für Die Reine Und
    Angewandte Mathematik</i>. De Gruyter. <a href="https://doi.org/10.1515/crelle-2026-0062">https://doi.org/10.1515/crelle-2026-0062</a>
  chicago: Browning, Timothy D, Efthymios Sofos, and Joni Teräväinen. “Bateman-Horn,
    Polynomial Chowla and the Hasse Principle with Probability.” <i>Journal Für Die
    Reine Und Angewandte Mathematik</i>. De Gruyter, 2026. <a href="https://doi.org/10.1515/crelle-2026-0062">https://doi.org/10.1515/crelle-2026-0062</a>.
  ieee: T. D. Browning, E. Sofos, and J. Teräväinen, “Bateman-Horn, polynomial Chowla
    and the Hasse principle with probability,” <i>Journal für die reine und angewandte
    Mathematik</i>. De Gruyter, 2026.
  ista: Browning TD, Sofos E, Teräväinen J. 2026. Bateman-Horn, polynomial Chowla
    and the Hasse principle with probability. Journal für die reine und angewandte
    Mathematik.
  mla: Browning, Timothy D., et al. “Bateman-Horn, Polynomial Chowla and the Hasse
    Principle with Probability.” <i>Journal Für Die Reine Und Angewandte Mathematik</i>,
    De Gruyter, 2026, doi:<a href="https://doi.org/10.1515/crelle-2026-0062">10.1515/crelle-2026-0062</a>.
  short: T.D. Browning, E. Sofos, J. Teräväinen, Journal Für Die Reine Und Angewandte
    Mathematik (2026).
corr_author: '1'
date_created: 2026-09-06T22:01:58Z
date_published: 2026-08-25T00:00:00Z
date_updated: 2026-09-09T13:28:45Z
day: '25'
department:
- _id: TiBr
doi: 10.1515/crelle-2026-0062
external_id:
  arxiv:
  - '2212.10373'
fulldoi: https://doi.org/10.1515/crelle-2026-0062
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2212.10373
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P32428
  name: New frontiers of the Manin conjecture
publication: Journal für die reine und angewandte Mathematik
publication_identifier:
  eissn:
  - 1435-5345
  issn:
  - 0075-4102
publication_status: epub_ahead
publisher: De Gruyter
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bateman-Horn, polynomial Chowla and the Hasse principle with probability
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2026'
...