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arXiv · 2201.01768

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

Jesse Thorner
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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 $\mathrm{Re}(s)=1$.

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Jesse Thorner. 2022-01-05. Effective quantum unique ergodicity for Hecke-Maass newforms and Landau-Siegel zeros. https://doi.org/10.1093/qmath/haab064

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