Strong subconvexity for self-dual $\mathrm{GL} (3)$ $L$-functions

TL;DR

This paper establishes strong subconvexity bounds for self-dual GL(3) L-functions in the t-aspect and for GL(3)×GL(2) L-functions in the spectral aspect, advancing understanding of their size and distribution.

Contribution

It proves the natural limit of the moment method for these L-functions, improving bounds in the critical line and spectral aspects.

Findings

Established strong subconvexity bounds in the t-aspect for self-dual GL(3) L-functions.

Derived subconvexity bounds in the spectral aspect for GL(3)×GL(2) L-functions.

Progressed towards the natural limit of the moment method for these L-functions.

Abstract

In this paper, we prove strong subconvexity bounds for self-dual $\mathrm{GL}(3)$ $L$-functions in the $t$-aspect and for $\mathrm{GL}(3)\times\mathrm{GL}(2)$ $L$-functions in the $\mathrm{GL}(2)$-spectral aspect. The bounds are strong in the sense that they are the natural limit of the moment method pioneered by Xiaoqing Li, modulo current knowledge on estimate for the second moment of $\rm GL(3)$ $L$-functions on the critical line.