---
OA_place: repository
OA_type: green
_id: '22200'
abstract:
- lang: eng
  text: "In Kuperberg and Lal´ın [Forum Math. 34 (2022), pp. 711–747],\r\nthe authors
    studied the mean-square of certain sums of the divisor function\r\ndk(f) over
    the function field Fq[T] in the limit as q →∞ and related these\r\nsums to integrals
    over the ensemble of symplectic matrices, along similar lines\r\nas previous work
    of Keating, Rodgers, Roditty-Gershon and Rudnick [Math. Z.\r\n288 (2018), pp.
    167–198] for unitary matrices. We present an analogous problem yielding an integral
    over the ensemble of orthogonal matrices and pursue\r\na more detailed study of
    both the symplectic and orthogonal matrix integrals,\r\nrelating them to symmetric
    function theory. The function field results lead to\r\nconjectures concerning
    analogous questions over number fields."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Vivian Zieve
  full_name: Kuperberg, Vivian Zieve
  id: c3bac823-112d-11f0-a3f5-c264f852e697
  last_name: Kuperberg
- first_name: Matilde
  full_name: Lalín, Matilde
  last_name: Lalín
citation:
  ama: Kuperberg VZ, Lalín M. Symplectic conjectures for sums of divisor functions
    and explorations of an orthogonal regime. <i>Transactions of the American Mathematical
    Society, Series B</i>. 2025;12(10):323-370. doi:<a href="https://doi.org/10.1090/btran/186">10.1090/btran/186</a>
  apa: Kuperberg, V. Z., &#38; Lalín, M. (2025). Symplectic conjectures for sums of
    divisor functions and explorations of an orthogonal regime. <i>Transactions of
    the American Mathematical Society, Series B</i>. American Mathematical Society.
    <a href="https://doi.org/10.1090/btran/186">https://doi.org/10.1090/btran/186</a>
  chicago: Kuperberg, Vivian Zieve, and Matilde Lalín. “Symplectic Conjectures for
    Sums of Divisor Functions and Explorations of an Orthogonal Regime.” <i>Transactions
    of the American Mathematical Society, Series B</i>. American Mathematical Society,
    2025. <a href="https://doi.org/10.1090/btran/186">https://doi.org/10.1090/btran/186</a>.
  ieee: V. Z. Kuperberg and M. Lalín, “Symplectic conjectures for sums of divisor
    functions and explorations of an orthogonal regime,” <i>Transactions of the American
    Mathematical Society, Series B</i>, vol. 12, no. 10. American Mathematical Society,
    pp. 323–370, 2025.
  ista: Kuperberg VZ, Lalín M. 2025. Symplectic conjectures for sums of divisor functions
    and explorations of an orthogonal regime. Transactions of the American Mathematical
    Society, Series B. 12(10), 323–370.
  mla: Kuperberg, Vivian Zieve, and Matilde Lalín. “Symplectic Conjectures for Sums
    of Divisor Functions and Explorations of an Orthogonal Regime.” <i>Transactions
    of the American Mathematical Society, Series B</i>, vol. 12, no. 10, American
    Mathematical Society, 2025, pp. 323–70, doi:<a href="https://doi.org/10.1090/btran/186">10.1090/btran/186</a>.
  short: V.Z. Kuperberg, M. Lalín, Transactions of the American Mathematical Society,
    Series B 12 (2025) 323–370.
date_created: 2026-06-29T12:59:46Z
date_published: 2025-03-20T00:00:00Z
date_updated: 2026-07-14T11:24:55Z
day: '20'
doi: 10.1090/btran/186
extern: '1'
external_id:
  arxiv:
  - '2212.04969'
intvolume: '        12'
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2212.04969
mathsc:
- 11N60
- 05A15
- 11M50
- 11N56
month: '03'
oa: 1
oa_version: Preprint
page: 323-370
publication: Transactions of the American Mathematical Society, Series B
publication_identifier:
  issn:
  - 2330-0000
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Symplectic conjectures for sums of divisor functions and explorations of an
  orthogonal regime
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 12
year: '2025'
...