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arXiv · 1404.6867

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

Jianya Liu·Jie Wu
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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 $\mbox{Re} s>1$. 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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Jianya Liu, Jie Wu. 2015-07-02. The number of coefficients of automorphic $L$-functions for $GL_m$ of same signs. https://arxiv.org/abs/1404.6867

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