Local behavior of arithmetical functions with applications to automorphic L-functions

Abstract : We derive a Voronoi-type series approximation for the local weighted mean of an arithmetical function that is associated to Dirichlet series satisfying a functional equation with gamma factors. The series is exploited to study the oscillation frequency with a method of Heath-Brown and Tsang [7]. A by-product is another proof for the well-known result of no element in the Selberg class of degree 0 < d < 1. Our major applications include the sign-change problem of the coefficients of automorphic L-functions for GL m , which improves significantly some results of Liu and Wu [14]. The cases of modular forms of half-integral weight and Siegel eigenforms are also considered.
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  • HAL Id : hal-01279192, version 2
  • ARXIV : 1602.09097

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Yuk-Kam Lau, Jianya Liu, Jie Wu. Local behavior of arithmetical functions with applications to automorphic L-functions. 2016. ⟨hal-01279192v2⟩

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