English

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

Number Theory 2022-10-28 v1

Abstract

We show that Landau-Siegel zeros for Dirichlet LL-functions do not exist or quantum unique ergodicity for GL2\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 LL-functions repel the zeros of all other automorphic LL-functions from the line Re(s)=1\mathrm{Re}(s)=1.

Keywords

Cite

@article{arxiv.2201.01768,
  title  = {Effective quantum unique ergodicity for Hecke-Maass newforms and Landau-Siegel zeros},
  author = {Jesse Thorner},
  journal= {arXiv preprint arXiv:2201.01768},
  year   = {2022}
}

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11 pages