标题：Moments of L-Functions Attached to the Twist of Modular Form by Dirichlet Characters
作者：Ji, Guanghua; Sun, Haiwei
作者机构：[Ji, G] School of Mathematics, Shandong University, Jinan, 250100, China;[ Sun, H] School of Mathematics and Statistics, Shandong University, Weihai, 更多
通讯作者地址：[Sun, HW]Shandong Univ, Sch Math & Stat, Weihai 264209, Shandong, Peoples R China.
关键词：Moments;Automorphic L-functions;Convexity theorem
摘要：Let f(z) be a holomorphic cusp form of weight. with respect to the full modular group SL2(Z). Let L(s, f) be the automorphic L-function associated with f(z) and chi be a Dirichlet character modulo q. In this paper, the authors prove that unconditionally for k = 1/n with n is an element of N,; M-k(q, f) = Sigma chi((mod q)chi not equal chi 0) vertical bar L (1/2, f circle times chi)vertical bar(2k) <=(k) phi(q) (log q)k(2); and the result also holds for any real number 0 < k < 1 under the GRH for L(s, f chi circle times). The authors also prove that under the GRH for L(s, f circle times chi),; M-k(q, f) >>(k) phi(q)(log q)(k2); for any real number k > 0 and any large prime q.