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

Let f and g be holomorphic cusp forms of weights k 1 and k 2 for the congruence subgroups Γ 0 ( N 1 ) and Γ 0 ( N 2), 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 k ε 1 ≪ k 2 ≪ k 1 1-ε . These bounds are the mean Lindelöf 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 + i t, 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 k 1 and k 2 aspects.