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.
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)。