Vol. 13, No. 8, 2019

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

Volume 17
Issue 10, 1681–1865
Issue 9, 1533–1680
Issue 8, 1359–1532
Issue 7, 1239–1357
Issue 6, 1127–1237
Issue 5, 981–1126
Issue 4, 805–980
Issue 3, 541–804
Issue 2, 267–539
Issue 1, 1–266

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
Subscriptions
 
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
Theta operators on unitary Shimura varieties

Ehud de Shalit and Eyal Z. Goren

Vol. 13 (2019), No. 8, 1829–1877
DOI: 10.2140/ant.2019.13.1829
Abstract

We define a theta operator on p-adic vector-valued modular forms on unitary groups of arbitrary signature, over a quadratic imaginary field in which p is inert. We study its effect on Fourier–Jacobi expansions and prove that it extends holomorphically beyond the μ-ordinary locus, when applied to scalar-valued forms.

Keywords
Shimura variety, theta operator, modular form
Mathematical Subject Classification 2010
Primary: 11G18
Secondary: 14G35
Milestones
Received: 1 January 2018
Revised: 9 January 2019
Accepted: 13 June 2019
Published: 9 October 2019
Authors
Ehud de Shalit
Einstein Institute of Mathematics
The Hebrew University of Jerusalem
Israel
Eyal Z. Goren
Department of Mathematics and Statistics
McGill University
Montreal
Canada