Moments of L-Functions Attached to the Twist of Modular Form by Dirichlet Characters  

作　　者：Guanghua JI Haiwei SUN 

机构地区：[1]School of Mathematics, Shandong University [2]School of Mathematics and Statistics, Shandong University

出　　处：《Chinese Annals of Mathematics,Series B》2015年第2期237-252,共16页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11301299);the Natural Science Foundation of Shandong Province(No.ZR2012AQ001);the Specialized Research Fund for the Doctoral Program of Higher Education(New Teachers)(Nos.20110131120001,20120131120075)

摘　　要：Let f（z） be a holomorphic cusp form of weight κ with respect to the full modular group SL2（Z）. Let L（s, f） be the automorphic L-function associated with f（z） and χ be a Dirichlet character modulo q. In this paper, the authors prove that unconditionally for k =1/n with n ∈ N,Mk（q,f）=∑χ（mod q）χ≠χ0｜L（1/2,f χ）｜^2k〈〈 kФ（q）（log q）^k^2, and the result also holds for any real number 0 〈 k 〈 1 under the GRH for L（s, f χ）.The authors also prove that under the GRH for L（s, f χ）,for any real number k 〉 0 and any large prime q.

关 键 词：MOMENTS Automorphic L-functions Convexity theorem 

分 类 号：O156[理学—数学]