---
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'
date_created: 2024-04-21T22:00:53Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2025-09-04T13:44:16Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1017/S1474748024000161
external_id:
  arxiv:
  - '2212.11038'
  isi:
  - '001200337400001'
file:
- access_level: open_access
  checksum: b300541d581a71d92314df5ae8c4cc09
  content_type: application/pdf
  creator: dernst
  date_created: 2025-01-09T08:56:33Z
  date_updated: 2025-01-09T08:56:33Z
  file_id: '18793'
  file_name: 2024_JournInstMathJussieu_Browning.pdf
  file_size: 690974
  relation: main_file
  success: 1
file_date_updated: 2025-01-09T08:56:33Z
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'
scopus_import: '1'
status: public
title: Generalised quadratic forms over totally real number fields
tmp:
  image: /images/cc_by.png
  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
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 23
year: '2024'
...