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

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

2011-06-25

arxiv.org/abs/1106.5110v4

Mathematics

Number Theory

16 pages. To appear in Math. Ann

Scientific paper

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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