Dirichlet $L$-functions on the critical line and multiplicative chaos

Sami Vihko

In this article, we prove that the Dirichlet $L$-functions $L(1/2+ix,{\chi }_q)$, where ${\chi }_q$ is a uniformly random Dirichlet character modulo $q$ and $x\in \mathbb{R}$, converge as $q\t…