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arXiv · 2507.17002

Certain Siegel Cusp Forms with Level are Determined by their Fundamental Fourier Coefficients

Sidney Washburn
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Abstract

We prove that vector-valued Siegel cusp forms for $\Gamma_0^n(N)$ with certain nebentypus are determined by their fundamental Fourier coefficients with discriminants coprime to the level $N$, assuming $N$ is odd and square-free. In the case of genus $3$, we strengthen this to Fourier coefficients corresponding to maximal orders in quaternion algebras. We also prove that Jacobi forms of fundamental index with discriminant coprime to the odd level $N$ are determined by their primitive theta components.

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Sidney Washburn. 2025-07-22. Certain Siegel Cusp Forms with Level are Determined by their Fundamental Fourier Coefficients. https://arxiv.org/abs/2507.17002

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