The angle of large values of $L$-functions

TL;DR

This paper establishes lower bound results for the size of central values of L-functions when their argument angles are restricted, advancing understanding of their extremal behavior.

Contribution

It provides new omega results for L-functions' central values under angle constraints, a novel restriction in the study of their size.

Findings

Proves omega results for L-functions with constrained angles

Shows extremal size behavior of L-values under angle restrictions

Enhances understanding of the distribution of L-values at the center

Abstract

We prove omega results for the central value of $L$-functions with the further condition that the angle is also constrained.