KMS Of Academy of mathematics and systems sciences, CAS
Two Linnik-type problems for automorphic L-functions | |
Liu, Jianya1; Qu, Yan2; Wu, Jie3 | |
2011-09-01 | |
Source Publication | MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY |
ISSN | 0305-0041 |
Volume | 151Pages:219-227 |
Abstract | 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 |
Language | 英语 |
Funding Project | Nancy-Universite ; NSFC |
WOS Research Area | Mathematics |
WOS Subject | Mathematics |
WOS ID | WOS:000294150900002 |
Publisher | CAMBRIDGE UNIV PRESS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/13125 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Liu, Jianya |
Affiliation | 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 |
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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