Further improvement on bounds for L-functions related to GL(3)

Let f be a fixed self-dual Hecke-Maass form for SL(3, Z), and let u be an even Hecke-Maass form for SL(2, Z) with Laplace eigenvalue 1/4 + k(2) , k > 0. A subconvexity bound for L(1/2, f x u) is improved to , O(k(21/16+epsilon))and a subconvexity bound for L(1/2+it, f) is improved to O((1 + vertical bar t vertical bar)(21/32+epsilon)) . New techniques employed include an application of an asymptotic formula by Salazar and Ye [Spectral square moments of a resonance sum for Maass forms, Front. Math. China 12(5) (2017) 1183-1200] to make error terms negligible, an iterative algorithm to locate stationary point, and a non-trivial estimation of Kloosterman sums.