Small-scale equidistribution of Hecke eigenforms at infinity

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We investigate the equidistribution of Hecke eigenforms for (Formula presented.) on sets that are shrinking toward the cusp. We show that at scales finer than the Planck scale they do not equidistribute while at scales more coarse than the Planck scale they equidistribute on a full density subsequence of eigenforms. On a suitable set of test functions we compute the variance showing an interesting transition behavior at half the Planck scale.

Original languageEnglish
JournalJournal of the London Mathematical Society
Volume106
Issue number3
Pages (from-to)2696-2729
ISSN0024-6107
DOIs
Publication statusPublished - 2022

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