Extreme values of $\arg L(1,\chi)$

TL;DR

This paper investigates the behavior of the argument of L-functions at 1 for primitive characters modulo large primes, focusing on the distribution of their extreme values.

Contribution

It provides new insights into the distribution and extremal behavior of the argument of L(1,χ) for primitive characters as the modulus grows.

Findings

Characterizes the distribution of extreme values of $ ext{arg} L(1, ext{χ})$

Identifies bounds for the maximum and minimum of $ ext{arg} L(1, ext{χ})$

Provides asymptotic estimates for the frequency of extreme values

Abstract

In this paper we study the distribution of extreme values of $\arg L(1,\chi)$, as $\chi$ varies over primitive characters modulo a large prime $q$.