The number of coefficients of automorphic L-functions for GL m of same signs
The number of coefficients of automorphic L-functions for GL m of same signs
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DOI：
10.1016/j.jnt.2014.09.020
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发表时间：
2014-04
影响因子：
0.7
通讯作者：
Jianya Liu;Jie Wu
中科院分区：
文献类型：
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作者：
Jianya Liu;Jie Wu
设π是GL m（AQ）的不可约酉尖点表示，L（s，π）是π的自守L-函数，它在半平面上有Dirichlet级数表达式.当π自逆时，狄利克雷级数表达式中的所有系数都是真实的。本文分别给出了正系数和负系数个数的非平凡下界。
Let π be an irreducible unitary cuspidal representation for GL m (A Q), and let L (s, π) be the automorphic L-function attached to π, which has a Dirichlet series expression in the half-plane ℜ e 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.