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Autor(in)
Datum
2022-08Typ
- Journal Article
ETH Bibliographie
yes
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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. Mehr anzeigen
Publikationsstatus
publishedExterne Links
Zeitschrift / Serie
International Mathematics Research NoticesBand
Seiten / Artikelnummer
Verlag
Oxford University PressOrganisationseinheit
09488 - Nelson, Paul D. (ehemalig) / Nelson, Paul D. (former)
ETH Bibliographie
yes
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