The number of coefficients of automorphic L-functions for GL_m of same signs

2014/04/28 by Liu, Jianya, Wu, Jie
#11F30 #11F66 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1404.6867

Abstract

Let π be an irreducible unitary cuspidal representation for GL_m(\Bbb A_{\Bbb Q}), and let L(s, π) be the automorphic L-function attached to π, which has a Dirichlet series expression in the half-plane Re s>1. When π is self-contragredient, all the coefficients in the Dirichlet series expression are real. In this paper we give non-trivial lower bounds for the number of positive and negative coefficients, respectively.

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