Vol. 15, No. 6, 2021

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

Volume 15
Issue 8, 1865–2122
Issue 7, 1593–1864
Issue 6, 1343–1592
Issue 5, 1077–1342
Issue 4, 821–1076
Issue 3, 569–820
Issue 2, 309–567
Issue 1, 1–308

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
This article is available for purchase or by subscription. See below.
Sato–Tate equidistribution for families of Hecke–Maass forms on $\mathrm{SL}(n,\mathbb{R}) / \mathrm{SO}(n)$

Jasmin Matz and Nicolas Templier

Vol. 15 (2021), No. 6, 1343–1428

We establish the Sato–Tate equidistribution of Hecke eigenvalues of the family of Hecke–Maass cusp forms on SL(n, )SL(n, )SO(n). As part of the proof, we establish a uniform upper-bound for spherical functions on semisimple Lie groups which is of independent interest. For each of the principal, symmetric square and exterior square L-functions, we deduce the level distribution with restricted support of the low-lying zeros. We also deduce average estimates toward Ramanujan, including an improvement on the previous literature in the case n = 2.

PDF Access Denied

However, your active subscription may be available on Project Euclid at

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

automorphic forms, $L$-functions, Arthur–Selberg trace formula
Mathematical Subject Classification
Primary: 11F70
Secondary: 20G30, 33C55, 43A90
Received: 1 September 2018
Revised: 24 November 2020
Accepted: 20 December 2020
Published: 16 October 2021
Jasmin Matz
Department of Mathematical Science
Universitetsparken 5
Nicolas Templier
Department of Mathematics
Cornell University
Ithaca, NY
United States