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

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2020,（5）
• 页码范围: 823-844
• 页数: 22页
• 语种: 英文

摘要

Let f and g be holomorphic cusp forms of weights k1 and k2 for the congruence subgroups Γ0(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 kε1 ＜＜ k2 ＜＜ k11-ε.These bounds are the mean Lindel(o)f 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.