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arXiv · 2103.13995

On sign changes of primitive Fourier coefficients of Siegel cusp forms

Karam Deo Shankhadhar·Prashant Tiwari
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Abstract

In this article, we establish quantitative results for sign changes in certain subsequences of primitive Fourier coefficients of a non-zero Siegel cusp form of arbitrary degree over congruence subgroups. As a corollary of our result for degree two Siegel cusp forms, we get sign changes of its diagonal Fourier coefficients. In the course of our proofs, we prove the non-vanishing of certain type of Fourier-Jacobi coefficients of a Siegel cusp form and all theta components of certain Jacobi cusp forms of arbitrary degree over congruence subgroups, which are also of independent interest.

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Karam Deo Shankhadhar, Prashant Tiwari. 2021-03-25. On sign changes of primitive Fourier coefficients of Siegel cusp forms. https://arxiv.org/abs/2103.13995

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