The circle method and bounds for $L$-functions - III: $t$-aspect subconvexity for GL(3) $L$-functions

TL;DR

This paper establishes a subconvexity bound for GL(3) $L$-functions in the $t$-aspect, improving the known bounds and advancing understanding of automorphic $L$-functions.

Contribution

It proves a new subconvex bound for $L(1/2+it, \,\pi)$ for GL(3) Maass forms, enhancing previous results in the $t$-aspect.

Findings

Proves $L(1/2+it,\pi) \ll (1+|t|)^{3/4 - 1/16 + \varepsilon}$.

Improves the exponent in the subconvexity bound for GL(3) $L$-functions.

Advances methods in analytic number theory for automorphic forms.

Abstract

Let $\pi$ be a Hecke-Maass cusp form for $SL(3,\mathbb Z)$. In this paper we will prove the following subconvex bound $$ L(\tfrac{1}{2}+it,\pi)\ll_{\pi,\varepsilon} (1+|t|)^{3/4-1/16+\varepsilon}. $$