---
OA_place: repository
OA_type: green
_id: '22204'
abstract:
- lang: eng
  text: "We study the distribution of consecutive sums of two squares in arithmetic
    progressions. We\r\nshow that for any odd squarefree modulus q, any two reduced
    congruence classes a1 and a2 mod q,\r\nand any r1,r2 ≥ 1, a positive density of
    sums of two squares begin a chain of r1 consecutive sums of\r\ntwo squares, all
    of which are a1 mod q, followed immediately by a chain of r2 consecutive sums
    of two\r\nsquares, all of which are a2 mod q. This is an analog of the result
    of Maynard for the sequence of primes,\r\nshowing that for any reduced congruence
    class a mod q and for any r ≥ 1, a positive density of primes\r\nbegin a sequence
    of r consecutive primes, all of which are a mod q"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Noam
  full_name: Kimmel, Noam
  last_name: Kimmel
- first_name: Vivian Zieve
  full_name: Kuperberg, Vivian Zieve
  id: c3bac823-112d-11f0-a3f5-c264f852e697
  last_name: Kuperberg
citation:
  ama: Kimmel N, Kuperberg VZ. Positive density for consecutive runs of sums of two
    squares. <i>Journal of the Institute of Mathematics of Jussieu</i>. 2025;24(5):1995-2046.
    doi:<a href="https://doi.org/10.1017/s1474748025000131">10.1017/s1474748025000131</a>
  apa: Kimmel, N., &#38; Kuperberg, V. Z. (2025). Positive density for consecutive
    runs of sums of two squares. <i>Journal of the Institute of Mathematics of Jussieu</i>.
    Cambridge University Press. <a href="https://doi.org/10.1017/s1474748025000131">https://doi.org/10.1017/s1474748025000131</a>
  chicago: Kimmel, Noam, and Vivian Zieve Kuperberg. “Positive Density for Consecutive
    Runs of Sums of Two Squares.” <i>Journal of the Institute of Mathematics of Jussieu</i>.
    Cambridge University Press, 2025. <a href="https://doi.org/10.1017/s1474748025000131">https://doi.org/10.1017/s1474748025000131</a>.
  ieee: N. Kimmel and V. Z. Kuperberg, “Positive density for consecutive runs of sums
    of two squares,” <i>Journal of the Institute of Mathematics of Jussieu</i>, vol.
    24, no. 5. Cambridge University Press, pp. 1995–2046, 2025.
  ista: Kimmel N, Kuperberg VZ. 2025. Positive density for consecutive runs of sums
    of two squares. Journal of the Institute of Mathematics of Jussieu. 24(5), 1995–2046.
  mla: Kimmel, Noam, and Vivian Zieve Kuperberg. “Positive Density for Consecutive
    Runs of Sums of Two Squares.” <i>Journal of the Institute of Mathematics of Jussieu</i>,
    vol. 24, no. 5, Cambridge University Press, 2025, pp. 1995–2046, doi:<a href="https://doi.org/10.1017/s1474748025000131">10.1017/s1474748025000131</a>.
  short: N. Kimmel, V.Z. Kuperberg, Journal of the Institute of Mathematics of Jussieu
    24 (2025) 1995–2046.
date_created: 2026-06-29T13:01:08Z
date_published: 2025-09-01T00:00:00Z
date_updated: 2026-07-14T11:50:36Z
day: '01'
doi: 10.1017/s1474748025000131
extern: '1'
external_id:
  arxiv:
  - '2406.04174'
intvolume: '        24'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2406.04174
month: '09'
oa: 1
oa_version: Preprint
page: 1995-2046
publication: Journal of the Institute of Mathematics of Jussieu
publication_identifier:
  eissn:
  - 1475-3030
  issn:
  - 1474-7480
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Positive density for consecutive runs of sums of two squares
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '15338'
abstract:
- lang: eng
  text: We introduce a new class of generalised quadratic forms over totally real
    number fields, which is rich enough to capture the arithmetic of arbitrary systems
    of quadrics over the rational numbers. We explore this connection through a version
    of the Hardy–Littlewood circle method over number fields.
acknowledgement: The authors are grateful to Jayce Getz for asking questions that
  set this project in motion and to the anonymous referee for useful comments. T.B.
  was supported by a FWF grant (DOI 10.55776/P32428) and by a grant from the Institute
  for Advanced Study School of Mathematics. L.B.P. was partially supported by NSF
  DMS-2200470 and DMS-1652173, and thanks the Hausdorff Centre for Mathematics for
  hosting research visits.
article_processing_charge: Yes (via OA deal)
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: Lillian B.
  full_name: Pierce, Lillian B.
  last_name: Pierce
- first_name: Damaris
  full_name: Schindler, Damaris
  last_name: Schindler
citation:
  ama: Browning TD, Pierce LB, Schindler D. Generalised quadratic forms over totally
    real number fields. <i>Journal of the Institute of Mathematics of Jussieu</i>.
    2024;23(6):2859-2912. doi:<a href="https://doi.org/10.1017/S1474748024000161">10.1017/S1474748024000161</a>
  apa: Browning, T. D., Pierce, L. B., &#38; Schindler, D. (2024). Generalised quadratic
    forms over totally real number fields. <i>Journal of the Institute of Mathematics
    of Jussieu</i>. Cambridge University Press. <a href="https://doi.org/10.1017/S1474748024000161">https://doi.org/10.1017/S1474748024000161</a>
  chicago: Browning, Timothy D, Lillian B. Pierce, and Damaris Schindler. “Generalised
    Quadratic Forms over Totally Real Number Fields.” <i>Journal of the Institute
    of Mathematics of Jussieu</i>. Cambridge University Press, 2024. <a href="https://doi.org/10.1017/S1474748024000161">https://doi.org/10.1017/S1474748024000161</a>.
  ieee: T. D. Browning, L. B. Pierce, and D. Schindler, “Generalised quadratic forms
    over totally real number fields,” <i>Journal of the Institute of Mathematics of
    Jussieu</i>, vol. 23, no. 6. Cambridge University Press, pp. 2859–2912, 2024.
  ista: Browning TD, Pierce LB, Schindler D. 2024. Generalised quadratic forms over
    totally real number fields. Journal of the Institute of Mathematics of Jussieu.
    23(6), 2859–2912.
  mla: Browning, Timothy D., et al. “Generalised Quadratic Forms over Totally Real
    Number Fields.” <i>Journal of the Institute of Mathematics of Jussieu</i>, vol.
    23, no. 6, Cambridge University Press, 2024, pp. 2859–912, doi:<a href="https://doi.org/10.1017/S1474748024000161">10.1017/S1474748024000161</a>.
  short: T.D. Browning, L.B. Pierce, D. Schindler, Journal of the Institute of Mathematics
    of Jussieu 23 (2024) 2859–2912.
corr_author: '1'
das_tickbox: '0'
date_created: 2024-04-21T22:00:53Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2026-07-29T09:57:08Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1017/S1474748024000161
external_id:
  arxiv:
  - '2212.11038'
  isi:
  - '001200337400001'
file:
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  creator: dernst
  date_created: 2025-01-09T08:56:33Z
  date_updated: 2025-01-09T08:56:33Z
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  file_size: 690974
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has_accepted_license: '1'
intvolume: '        23'
isi: 1
issue: '6'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 2859-2912
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P32428
  name: New frontiers of the Manin conjecture
publication: Journal of the Institute of Mathematics of Jussieu
publication_identifier:
  eissn:
  - 1475-3030
  issn:
  - 1474-7480
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Generalised quadratic forms over totally real number fields
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  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
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...