---
OA_place: repository
OA_type: green
_id: '22194'
abstract:
- lang: eng
  text: "In [J. P. Keating, B. Rodgers, E. Roditty-Gershon and Z. Rudnick, Sums of
    divisor functions in \U0001D53D\U0001D45E⁢[\U0001D461] and matrix integrals, Math.
    Z. 288 2018, 1–2, 167–198], the authors established relationships of the mean-square
    of sums of the divisor function \U0001D451\U0001D458⁢(\U0001D453) over short intervals
    and over arithmetic progressions for the function field \U0001D53D\U0001D45E⁢[\U0001D447]
    to certain integrals over the ensemble of unitary matrices. We consider similar
    problems leading to distributions over the ensemble of symplectic matrices. We
    also consider analogous questions involving convolutions of the von Mangoldt function."
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. Sums of divisor functions and von Mangoldt convolutions
    in \U0001D53Dq[T] leading to symplectic distributions. <i>Forum Mathematicum</i>.
    2022;34(3):711-747. doi:<a href=\"https://doi.org/10.1515/forum-2021-0171\">10.1515/forum-2021-0171</a>"
  apa: "Kuperberg, V. Z., &#38; Lalín, M. (2022). Sums of divisor functions and von
    Mangoldt convolutions in \U0001D53Dq[T] leading to symplectic distributions. <i>Forum
    Mathematicum</i>. De Gruyter. <a href=\"https://doi.org/10.1515/forum-2021-0171\">https://doi.org/10.1515/forum-2021-0171</a>"
  chicago: "Kuperberg, Vivian Zieve, and Matilde Lalín. “Sums of Divisor Functions
    and von Mangoldt Convolutions in \U0001D53Dq[T] Leading to Symplectic Distributions.”
    <i>Forum Mathematicum</i>. De Gruyter, 2022. <a href=\"https://doi.org/10.1515/forum-2021-0171\">https://doi.org/10.1515/forum-2021-0171</a>."
  ieee: "V. Z. Kuperberg and M. Lalín, “Sums of divisor functions and von Mangoldt
    convolutions in \U0001D53Dq[T] leading to symplectic distributions,” <i>Forum
    Mathematicum</i>, vol. 34, no. 3. De Gruyter, pp. 711–747, 2022."
  ista: "Kuperberg VZ, Lalín M. 2022. Sums of divisor functions and von Mangoldt convolutions
    in \U0001D53Dq[T] leading to symplectic distributions. Forum Mathematicum. 34(3),
    711–747."
  mla: "Kuperberg, Vivian Zieve, and Matilde Lalín. “Sums of Divisor Functions and
    von Mangoldt Convolutions in \U0001D53Dq[T] Leading to Symplectic Distributions.”
    <i>Forum Mathematicum</i>, vol. 34, no. 3, De Gruyter, 2022, pp. 711–47, doi:<a
    href=\"https://doi.org/10.1515/forum-2021-0171\">10.1515/forum-2021-0171</a>."
  short: V.Z. Kuperberg, M. Lalín, Forum Mathematicum 34 (2022) 711–747.
date_created: 2026-06-29T12:57:26Z
date_published: 2022-03-26T00:00:00Z
date_updated: 2026-07-14T11:02:45Z
day: '26'
doi: 10.1515/forum-2021-0171
extern: '1'
external_id:
  arxiv:
  - '2107.01437'
intvolume: '        34'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2107.01437
month: '03'
oa: 1
oa_version: Preprint
page: 711-747
publication: Forum Mathematicum
publication_identifier:
  eissn:
  - 1435-5337
  issn:
  - 0933-7741
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
scopus_import: '1'
status: public
title: "Sums of divisor functions and von Mangoldt convolutions in \U0001D53Dq[T]
  leading to symplectic distributions"
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 34
year: '2022'
...