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

Abstract

Let [Formula: see text] be a fixed self-dual Hecke–Maass form for [Formula: see text], and let [Formula: see text] be an even Hecke–Maass form for [Formula: see text] with Laplace eigenvalue [Formula: see text], [Formula: see text]. A subconvexity bound for [Formula: see text] is improved to [Formula: see text], and a subconvexity bound for [Formula: see text] is improved to [Formula: see text]. 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.