Download this article
 Download this article For screen
For printing
Recent Issues

Volume 18
Issue 6, 1039–1219
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
Equidistribution theorems for holomorphic Siegel cusp forms of general degree: the level aspect

Henry H. Kim, Satoshi Wakatsuki and Takuya Yamauchi

Vol. 18 (2024), No. 5, 993–1038

This paper is an extension of Kim et al. (2020a), and we prove equidistribution theorems for families of holomorphic Siegel cusp forms of general degree in the level aspect. Our main contribution is to estimate unipotent contributions for general degree in the geometric side of Arthur’s invariant trace formula in terms of Shintani zeta functions in a uniform way. Several applications, including the vertical Sato–Tate theorem and low-lying zeros for standard L-functions of holomorphic Siegel cusp forms, are discussed. We also show that the “nongenuine forms”, which come from nontrivial endoscopic contributions by Langlands functoriality classified by Arthur, are negligible.

trace formula, holomorphic Siegel modular forms, equidistribution theorems, standard $L$-functions
Mathematical Subject Classification
Primary: 11F46, 11F70, 22E55, 11R45
Received: 26 October 2022
Revised: 17 April 2023
Accepted: 29 May 2023
Published: 16 April 2024
Henry H. Kim
Department of Mathematics
University of Toronto
Toronto, ON
Korea Institute for Advanced Study
Satoshi Wakatsuki
Faculty of Mathematics and Physics
Institute of Science and Engineering
Kanazawa University
Takuya Yamauchi
Mathematical Institute
Tohoku University

Open Access made possible by participating institutions via Subscribe to Open.