Open Access

Sturm bounds for Siegel modular forms

Research in Number Theory20151:5

DOI: 10.1007/s40993-015-0008-4

Received: 29 January 2015

Accepted: 2 February 2015

Published: 6 July 2015

Abstract

We establish Sturm bounds for degree g Siegel modular forms modulo a prime p, which are vital for explicit computations. Our inductive proof exploits Fourier-Jacobi expansions of Siegel modular forms and properties of specializations of Jacobi forms to torsion points. In particular, our approach is completely different from the proofs of the previously known cases g=1,2, which do not extend to the case of general g.

MSC 2010: Primary 11F46; Secondary 11F33