Distribution of Values of Symmetric power L-functions at the Edge of the Critical Strip

TL;DR

This paper investigates the distribution and bounds of symmetric power L-functions at the critical edge, providing new insights and generalizations that improve upon previous results in the field.

Contribution

It offers new bounds, distribution results, and extends existing conjectures for symmetric power L-functions at the critical point.

Findings

Bounds on symmetric power L-functions at s=1

Distribution functions for these values

Extensions of Montgomery-Vaughan's conjecture

Abstract

We study some problems on the distribution of values of symmetric power $L$-functions at $s=1$ in both aspects of level and weight: bounds of these values, extreme values, Montgomery-Vaughan's conjecture and distribution functions. Our results generalize and/or improve related results of Royer-Wu, Cogdell-Michel, Lau-Wu and Liu-Royer-Wu.