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Siegel cusp forms of degree 2 are determined by their fundamental Fourier coefficients

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Abstract

We prove that a Siegel cusp form of degree 2 for the full modular group is determined by its set of Fourier coefficients a(S) with 4 det(S) ranging over odd squarefree integers. As a key step to our result, we also prove that a classical cusp form of half-integral weight and level 4N, with N odd and squarefree, is determined by its set of Fourier coefficients a(d) with d ranging over odd squarefree integers, a result that was previously known only for Hecke eigenforms.

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  1. ETH Zürich, D-MATH, Rämistrasse 101, 8092, Zurich, Switzerland

    Abhishek Saha

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  1. Abhishek Saha
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Saha, A. Siegel cusp forms of degree 2 are determined by their fundamental Fourier coefficients. Math. Ann. 355, 363–380 (2013). https://doi.org/10.1007/s00208-012-0789-x

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  • DOI: https://doi.org/10.1007/s00208-012-0789-x

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