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

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 $\re s>\tfrac{1}{2}$. This exhibits a high fluctuation of the coefficients at squarefree integers.
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  • HAL Id : hal-01280172, version 2
  • ARXIV : 1602.08924

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Y.-J Jiang, Y.-K Lau, Emmanuel Royer, J Wu. On Fourier coefficients of modular forms of half integral weight at squarefree integers. 2016. ⟨hal-01280172v2⟩

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