ON FOURIER COEFFICIENTS OF MODULAR FORMS OF HALF INTEGRAL WEIGHT AT SQUAREFREE INTEGERS

Yujiao Jiang (1) , Yuk-Kam Lau (2) , Guangshi Lü (1) , Emmanuel Royer (3) , Jie Wu (4)

1 Shandong University
2 Department of Mathematics
3 LMBP - Laboratoire de Mathématiques Blaise Pascal
4 IECL - Institut Élie Cartan de Lorraine

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.

Domaines: Théorie des nombres [math.NT]

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⟩