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Two Linnik-type problems for automorphic L-functions
Liu, Jianya1; Qu, Yan2; Wu, Jie3
2011-09-01
Source PublicationMATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
ISSN0305-0041
Volume151Pages:219-227
AbstractLet 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.
DOI10.1017/S0305004111000314
Language英语
Funding ProjectNancy-Universite ; NSFC
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000294150900002
PublisherCAMBRIDGE UNIV PRESS
Citation statistics
Cited Times:5[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/13125
Collection中国科学院数学与系统科学研究院
Affiliation1.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
Recommended Citation
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.
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