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arXiv · 2104.00401

Non-vanishing of theta components of Jacobi forms with level and an application

Pramath Anamby
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Abstract

We prove that a non--zero Jacobi form of arbitrary level $N$ and square--free index $m_1m_2$ with $m_1|N$ and $(N,m_2)=1$ has a non--zero theta component $h_\mu$ with either $(\mu,2m_1m_2)=1$ or $(\mu,2m_1m_2)\nmid 2m_2$. As an application, we prove that a non--zero Siegel cusp form $F$ of degree $2$ and an odd level $N$ in the Atkin--Lehner type newspace is determined by fundamental Fourier coefficients up to a divisor of $N$.

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Pramath Anamby. 2021-04-01. Non-vanishing of theta components of Jacobi forms with level and an application. https://arxiv.org/abs/2104.00401

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