A new bound K2/3+ɛ for Rankin-Selberg ℒ-functions for Hecke congruence subgroups

  title={A new bound K2/3+ɛ for Rankin-Selberg ℒ-functions for Hecke congruence subgroups},
  author={Yuk-kam. Lau and Jianya Liu and Yangbo Ye},
Let f be a holomorphic Hecke eigenform for Γ0(N ) of weight k, or a Maass eigenform for Γ0(N ) with Laplace eigenvalue 1/4 + k. Let g be a fixed holomorphic or Maass cusp form for Γ0(N ). A subconvexity bound for central values of the Rankin-Selberg L-function L(s, f ⊗ g) is proved in the k-aspect: L(1/2+ it, f ⊗ g) N ,g,t,e k, while a convexity bound is only k. This new bound improves earlier subconvexity bounds for these Rankin-Selberg L-functions by Sarnak, the authors, and Blomer… 
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