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

Research paper by Y. -J Jiang, Y. -K Lau, Emmanuel Royer, J Wu

Indexed on: 20 Apr '16Published on: 20 Apr '16Published in: Mathematics - Number Theory



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.