Lower bounds for moments of quadratic twisted self-dual $\textrm{GL}(3)$ central $L$-values

TL;DR

This paper establishes the conjectured lower bounds for the moments of quadratic twisted self-dual GL(3) L-functions at the center, advancing understanding of their value distribution.

Contribution

It proves the conjectured order lower bounds for all moments of these L-functions, extending previous work on the first moment to all moments.

Findings

Confirmed the conjectured lower bounds for moments of GL(3) L-functions

Extended previous results from the first moment to all moments

Provided new insights into the distribution of these L-values

Abstract

In this paper, we prove the conjectured order lower bound for the $k$-th moment of central values of quadratic twisted self-dual $\textrm{GL}(3)$ $L$-functions for all $k\geq 1$, based on our recent work on the twisted first moment of central values in this family of $L$-functions.