New variants of arithmetic quantum ergodicity

Abstract

We establish two new variants of arithmetic quantum ergodicity. The first is for self-dual ${\mathrm{GL}}_2$ Hecke-Maass newforms over $\mathbb{Q}$ as the level and Laplace eigenvalue vary jointly. The second is a nonsplit analogue wherein almost all restrictions of Hilbert (respectively Bianchi) Hecke-Maass cusp forms to the modular surface dissipate as their Laplace eigenvalues grow.

31 pages

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