Quadratic Hecke Sums and Mass Equidistribution

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Abstract

We consider the analogue of the quantum unique ergodicity conjecture for holomorphic Hecke eigenforms on compact arithmetic hyperbolic surfaces. We show that this conjecture follows from nontrivial bounds for Hecke eigenvalues summed over quadratic progressions. Our reduction provides an analogue for the compact case of a criterion established by Luo–Sarnak for the case of the non-compact modular surface. The novelty is that known proofs of such criteria have depended crucially upon Fourier expansions, which are not available in the compact case. Unconditionally, we establish a twisted variant of the Holowinsky–Soundararajan theorem involving restrictions of normalized Hilbert modular forms arising via base change.

OriginalsprogEngelsk
TidsskriftInternational Mathematics Research Notices
Vol/bind2022
Nummer17
Sider (fra-til)13659-13701
Antal sider43
ISSN1073-7928
DOI
StatusUdgivet - aug. 2022
Udgivet eksterntJa

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