Selberg's Central Limit Theorem for Dirichlet $L$-functions of $q$-aspect

TL;DR

This paper provides a straightforward proof of Selberg's central limit theorem for Dirichlet L-functions in the q-aspect, utilizing the method developed by Radiwi extl{}l and Soundararajan.

Contribution

It introduces a simplified proof of Selberg's CLT for Dirichlet L-functions in the q-aspect, building on existing methods.

Findings

Proof of Selberg's CLT for Dirichlet L-functions in q-aspect

Simplification of the existing proof technique

Validation of the method's effectiveness in this context

Abstract

We give a simple proof of Selberg's central limit theorem for Dirichlet $L$-functions for $q$-aspect by following the method established by Radiwi\l\l\space and Soundararajan.