Equidistribution of the eigenvalues of Hecke operators

Dohoon Choi, Min Lee, Youngmin Lee and Subong Lim

Mathematische Nachrichten, 2025, vol. 298, issue 9, 3210-3246

Abstract: In this paper, we prove the equidistribution of the Hecke eigenvalues of Maass forms over an arbitrary number field at a fixed prime ideal, with respect to the Sato–Tate measure. As an application, we obtain that the proportion of Maass forms that do not satisfy the Ramanujan–Petersson conjecture at a fixed prime ideal is 0.

Date: 2025
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