Double square moments and subconvexity bounds for Rankin-Selberg L-functions of holomorphic cusp forms  

作　　者：Jianya Liu Haiwei Sun Yangbo Ye 

机构地区：[1]School of Mathematics,Shandong University,Jinan 250100,China [2]School of Mathematics and Statistics,Shandong University,Weihai 264209,China [3]Department of Mathematics,The University of Iowa,Iowa City,IA 52242-1419,USA

出　　处：《Science China Mathematics》2020年第5期823-844,共22页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11531008);Ministry of Education of China(Grant No.IRT16R43);Taishan Scholar Project of Shandong Province;supported by National Natural Science Foundation of China(Grant No.11601271);China Postdoctoral Science Foundation(Grant No.2016M602125);China Scholarship Council(Grant No.201706225004)。

摘　　要：Let f and g be holomorphic cusp forms of weights k1 and k2 for the congruence subgroups TO(N1)and Γ0(N2),respectively.In this paper the square moment of the Rankin-Selberg L-function for f and g in the aspect of both weights in short intervals is bounded,when k1^ε <<k^2<<k1^1-ε.These bounds are the mean Lindelof hypothesis in one case and subconvexity bounds on average in other cases.These square moment estimates also imply subconvexity bounds for individual L(1/2+it,f×g) for all g when f is chosen outside a small exceptional set.In the best case scenario the subconvexity bound obtained reaches the Weyl-type bound proved by Lau et al.(2006) in both the k1 and k2 aspects.

关 键 词：automorphic L-function congruence subgroup cusp form holomorphic cusp form Rankin-Selberg L-function square moment subconvexity bound 

分 类 号：O174[理学—数学]