标题:Two Linnik-type problems for automorphic L-functions
作者:Liu, J.;Qu, Y.;Wu, J.
作者机构:School of Mathematics, Shandong University, Jinan, Shandong 250100, China;Institute of Mathematics, Chinese Academy of Sciences
来源:Mathematical Proceedings of the Cambridge Philosophical Society
出版年:2011
期:2
页码:219-227
摘要:Let m ≥ 2 be an integer, and φ an irreducible unitary cuspidal representation for GLm(AQ), whose attached automorphic L-function is denoted by L(s, p). Let {a (n)}8n =1 be the sequence of coefficients in the Dirichlet series expression of L(s, p) in the half-plane Rs > 1. It is proved in this paper that, if p is such that the sequence {?p (n)}8n =1 is real, then the first sign change in the sequence {?p (n)}8n =1 occurs at some n Q1+e p, where Qp is the conductor of p, and the implied constant depends only on m and e. This improves the previous bound with the above exponent 1 + e replaced by m/2 + e. A result of the same quality is also established for {(n)ap (n)}8n =1, the sequence of coefficients in the Dirichlet series expression of -(L/L)(s, p) in the half-plane Rs ≥ 1.
资源类型:期刊论文
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