Effective quantum unique ergodicity for Hecke-Maass newforms and Landau-Siegel zeros

Abstract

We show that Landau-Siegel zeros for Dirichlet $L$-functions do not exist or quantum unique ergodicity for $\mathrm{GL}_2$ Hecke-Maass newforms holds with an effective rate of convergence. This follows from a more general result: Landau-Siegel zeros of Dirichlet $L$-functions repel the zeros of all other automorphic $L$-functions from the line $\mathrm{Re}(s)=1$.