On mod p properties of Siegel modular forms

We prove two results on mod p properties of Siegel modular forms. First, we use theta series in order to construct of a Siegel modular form of weight p−1 which is congruent to 1 mod p. Second, we define a theta operator on q-expansions and show that the algebra of Siegel modular forms mod p is stabl...

Full description

Saved in:
Bibliographic Details
Published in:Mathematische annalen 2007-06, Vol.338 (2), p.421-433
Main Authors: Böcherer Siegfried, Nagaoka Shoyu
Format: Article
Language:English
Subjects:
Analytic functions
Modular construction
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove two results on mod p properties of Siegel modular forms. First, we use theta series in order to construct of a Siegel modular form of weight p−1 which is congruent to 1 mod p. Second, we define a theta operator on q-expansions and show that the algebra of Siegel modular forms mod p is stable under , by exploiting the relation between and generalized Rankin-Cohen brackets.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-007-0081-7