Sturm Bounds for Siegel Modular Forms

2015/01/30 by Richter, Olav K., Westerholt-Raum, Martin
#FOS: Mathematics #Number Theory (math.NT) #Primary 11F46 #Secondary 11F33

paper · doi:10.48550/arxiv.1501.07733

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.

Related

• Sturm bounds for Siegel modular forms of degree 2 and odd weights
• Sturm type theorem for Siegel modular forms of degree 2
• Bounds for Siegel Modular Forms of genus 2 modulo p
• Improved bounds for Fourier coefficients of Siegel modular forms
• New bounds for fundamental Fourier coefficients of Siegel modular forms