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

Sami Vihko

In this paper we prove that the Dirichlet $L$-functions $L(1/2+ix,\ddot{I}{‡}_q)$, where $\ddot{I}{‡}_q$ is uniformly random Dirichlet character modulo $q$ and $x\in \mathbb{R}$, converges to a rand…