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 \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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2016
- DOI:
- 10.48550/arXiv.1602.09097
- arXiv:
- arXiv:1602.09097
- Bibcode:
- 2016arXiv160209097L
- Keywords:
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- Mathematics - Number Theory