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
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Acknowledgments
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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The authors declare that they have no competing interests.
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OKR and MW-R performed research and wrote the paper. Both authors read and approved the final manuscript.
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Richter, O.K., Westerholt-Raum, M. Sturm bounds for Siegel modular forms. Res. number theory 1, 5 (2015). https://doi.org/10.1007/s40993-015-0008-4
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DOI: https://doi.org/10.1007/s40993-015-0008-4
Keywords
- Modular Form
- Jacobi Form
- Fourier Series Expansion
- Torsion Point
- Siegel Modular Form