Local Behavior of Arithmetical Functions with Applications to Automorphic L-Functions
Number Theory
2016-03-08 v2
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 \textless{} d \textless{} 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.
Keywords
Cite
@article{arxiv.1602.09097,
title = {Local Behavior of Arithmetical Functions with Applications to Automorphic L-Functions},
author = {Yuk-Kam Lau and Jianya Liu and Jie Wu},
journal= {arXiv preprint arXiv:1602.09097},
year = {2016}
}