On a conjecture of Montgomery-Vaughan on extreme values of automorphic L-functions at 1

TL;DR

This paper proves a weaker version of Montgomery-Vaughan's conjecture concerning the extreme values of automorphic L-functions at 1, advancing understanding of their behavior.

Contribution

It introduces a partial proof of the conjecture, providing new insights into the distribution of automorphic L-functions at critical points.

Findings

Established a weaker form of the conjecture

Demonstrated bounds on automorphic L-functions at 1

Enhanced understanding of L-function extremal behavior

Abstract

In this paper, we prove a weaker form of a conjecture of Montgomery-Vaughan on extreme values of automorphic L-functions at 1.