A note on the number of coefficients of automorphic $L-$functions for $G{L}_m$ with same signs

Abstract

Let $\pi$ be an irreducible unitary cuspidal representation of $G{L}_m({\mathbb{A}}_{\mathbb{Q}})$ and $L(s,\pi )$ be the global $L-$function attached to $\pi$. If $\mathrm{Re}(s)>1$, $L(s,\pi )$ has a Dirichlet series expression. When $\pi$ is self-contragradient, all the coefficients of Dirichlet series are real. In this note, we shall give non-trivial lower bounds for the number of positive and negative coefficients respectively, which is an improvement on the recent work of Jianya Liu and Jie Wu.

References in corpus (1)

• The number of coefficients of automorphic $L$-functions for $G{L}_m$ of same signs

Cited by in corpus (1)

• The number of coefficients of automorphic $L$-functions for $G{L}_m$ of same signs