Second Moment of Degree Three L-Functions

Abstract

Let F be a Hecke-Maaß cusp form for SL(3, Z). In this dissertation, we obtain a nontrivial upper bound of the second moment of L(F, s) in the t-aspect:Z 2TT|L(F, 1/2 + it)|2dt ≪F,ϵ T3/2−3/32+ϵ. Immediate corollaries include improvements over the existing results on the Subconvexity bound for self-dual GL(3) L-functions in the t-aspect and for self-dual GL(3) × GL(2) Lfunctions in the GL(2) spectral aspect, the error term in the Rankin-Selberg problem, and the zero density estimate for GL(3) L-functions.