Effective Quantum Unique Ergodicity for Hecke–Maass Newforms and Landau–Siegel Zeros

Abstract

Abstract We show that Landau–Siegel zeros for Dirichlet L-functions do not exist or that 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 $\mathrm{Re}(s)=1$.