Vol. 7, No. 4, 2013

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
An analogue of Sturm's theorem for Hilbert modular forms

Yuuki Takai

Vol. 7 (2013), No. 4, 1001–1018
Abstract

In this paper, we consider congruences of Hilbert modular forms. Sturm showed that mod elliptic modular forms of weight k and level Γ1(N) are determined by the first (k12)[Γ1(1) : Γ1(N)] mod Fourier coefficients. We prove an analogue of Sturm’s result for Hilbert modular forms associated to totally real number fields. The proof uses the positivity of ample line bundles on toroidal compactifications of Hilbert modular varieties.

Keywords
Hilbert modular forms and varieties, congruences of modular forms, Sturm's theorem, toroidal and minimal compactifications, intersection numbers
Mathematical Subject Classification 2010
Primary: 11F41
Secondary: 11F30, 11F33, 14C17
Milestones
Received: 22 November 2011
Revised: 30 August 2012
Accepted: 4 September 2012
Published: 29 August 2013
Authors
Yuuki Takai
Graduate School of Mathematical Sciences
University of Tokyo
3-8-1 Komaba
Meguro, Tokyo, 153-8914
Japan