Sturm bounds for Siegel modular forms
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
KeywordsModular Form Jacobi Form Fourier Series Expansion Torsion Point Siegel Modular Form
The first author was partially supported by Simons Foundation Grant #200765. The second author thanks the Max Planck Institute for Mathematics for their hospitality. The paper was partially written, while the second author was supported by the ETH Zurich Postdoctoral Fellowship Program and by the Marie Curie Actions for People COFUND Program.
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