Vol. 13, No. 8, 2019

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

Volume 13
Issue 8, 1765–1981
Issue 7, 1509–1763
Issue 6, 1243–1507
Issue 5, 995–1242
Issue 4, 749–993
Issue 3, 531–747
Issue 2, 251–530
Issue 1, 1–249

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
Subscriptions
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
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