Two Linnik-type problems for automorphic L-functions

doi:10.1017/S0305004111000314

CSpace

	Two Linnik-type problems for automorphic L-functions
	Liu, Jianya 1; Qu, Yan 2; Wu, Jie 3
	2011-09-01
发表期刊	MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
ISSN	0305-0041
卷号	151 页码:219-227
摘要	Let m >= 2 be an integer, and pi an irreducible unitary cuspidal representation for GL(m)(A(Q)), whose attached automorphic L-function is denoted by L(s, pi). Let {lambda(pi) (n)(n=1)(infinity) be the sequence of coefficients in the Dirichlet series expression of L(s, pi) in the half-plane Rs > 1. It is proved in this paper that, if pi is such that the sequence {lambda(pi) (n)(n=1)(infinity) is real, then the first sign change in the sequence {lambda(pi) (n)}(n=1)(infinity) occurs at some n << Q(pi)(1+epsilon), where Q(pi) is the conductor of pi, and the implied constant depends only on m and epsilon. This improves the previous bound with the above exponent 1 + epsilon replaced by m/2 + epsilon. A result of the same quality is also established for {A (n)a(pi) (n)(r=1)(infinity), the sequence of coefficients in the Dirichlet series expression of - (L' / L)(s, 7) in the half-plane Rs > 1.
DOI	10.1017/S0305004111000314
语种	英语
资助项目	Nancy-Universite ; NSFC
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000294150900002
出版者	CAMBRIDGE UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/13125
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, Jianya
作者单位	1.Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China 2.Chinese Acad Sci, Inst Math, Beijing 100190, Peoples R China 3.Nancy Univ, CNRS, IECN, INRIA, F-54506 Vandoeuvre Les Nancy, France
推荐引用方式 GB/T 7714	Liu, Jianya,Qu, Yan,Wu, Jie. Two Linnik-type problems for automorphic L-functions[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY,2011,151:219-227.
APA	Liu, Jianya,Qu, Yan,&Wu, Jie.(2011).Two Linnik-type problems for automorphic L-functions.MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY,151,219-227.
MLA	Liu, Jianya,et al."Two Linnik-type problems for automorphic L-functions".MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY 151(2011):219-227.