Subconvexity Bounds for GL(3) Automorphic L-Functions and the Generalized Lindelöf Hypothesis

The subconvexity problem for automorphic L-functions on higher rank groups remains one of the central challenges in analytic number theory, serving as a critical testing ground for the Generalized Lindelöf Hypothesis (GLH). In this monograph, we establish a new subconvex bound for the L-function L(s, ) associated with a self-dual Hecke-Maass cusp form for SL(3, Z) in the t-aspect. Specifically, we prove that L(1/2 + it, ) , (1+|t|)3/4 - + for a computable constant > 0, improving upon the convexity bound of 3/4 implied by the Phragmén-Lindelöf principle. Our method synthesizes the GL(3) Voronoi summation formula with an advanced delta-symbol method, effectively separating the oscillating factors in the shifted convolution sums. We further discuss the implications of this result for the GLH and the non-vanishing of central L-values, providing a rigorous pathway toward breaking the barrier of 3/4 for general GL(n) automorphic forms.