On Fourier coefficients of modular forms of half integral weight at squarefree integers

Y. -J Jiang; Y. -K Lau; Emmanuel Royer; J Wu

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arXiv · 1602.08924

On Fourier coefficients of modular forms of half integral weight at squarefree integers

Y. -J Jiang·Y. -K Lau·Emmanuel Royer·J Wu

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Abstract

We show that the Dirichlet series associated to the Fourier coefficients of a half-integral weight Hecke eigenform at squarefree integers extends analytically to a holomorphic function in the half-plane $\re s\textgreater{}\tfrac{1}{2}$. This exhibits a high fluctuation of the coefficients at squarefree integers.

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Y. -J Jiang, Y. -K Lau, Emmanuel Royer, J Wu. 2016-02-29. On Fourier coefficients of modular forms of half integral weight at squarefree integers. https://arxiv.org/abs/1602.08924

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