Short second moment bound and Subconvexity for GL(3) $L$-functions

TL;DR

This paper establishes a short second moment bound for GL(3) L-functions, leading to a subconvexity estimate that improves the known bounds on the growth of these L-functions along the critical line.

Contribution

It introduces a novel short second moment bound for GL(3) L-functions, resulting in a new subconvexity estimate along the critical line.

Findings

Proves a subconvexity bound of (1+|t|)^{3/4 - 1/8 + ε} for GL(3) L-functions.

Develops a short second moment method tailored for high-rank L-functions.

Enhances understanding of the growth of automorphic L-functions on the critical line.

Abstract

Let $\pi$ be a Hecke cusp form for $\mathrm{SL}_3(\mathbb{Z})$. We bound the second moment average of $L(s,\pi)$ over a short interval to obtain the subconvexity estimate $$ L(1/2+it, \pi) \ll_{\pi, \varepsilon} (1+|t|)^{3/4-1/8+\varepsilon}. $$