Sturm bounds for Siegel modular forms
© Richter and Westerholt-Raum.; licensee Springer. 2015
Received: 29 January 2015
Accepted: 2 February 2015
Published: 6 July 2015
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