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 > 1 2. This exhibits a high fluctuation of the coefficients at squarefree integers.
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Submitted on : Monday, February 29, 2016 - 10:39:51 AM
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  • HAL Id : hal-01280172, version 1
  • ARXIV : 1602.08924

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Yujiao Jiang, Yuk-Kam Lau, Guangshi Lü, Emmanuel Royer, Jie Wu. ON FOURIER COEFFICIENTS OF MODULAR FORMS OF HALF INTEGRAL WEIGHT AT SQUAREFREE INTEGERS. 2016. ⟨hal-01280172v1⟩

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