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arXiv · 1405.0643

A note on the number of coefficients of automorphic $L-$functions for $GL_m$ with same signs

Chaohua Jia
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Abstract

Let $\pi$ be an irreducible unitary cuspidal representation of $GL_m({\Bbb A}_{\Bbb Q})$ and $L(s,\,\pi)$ be the global $L-$function attached to $\pi$. If ${\rm Re}(s)>1$, $L(s,\,\pi)$ 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.

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Chaohua Jia. 2014-05-04. A note on the number of coefficients of automorphic $L-$functions for $GL_m$ with same signs. https://arxiv.org/abs/1405.0643

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