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.
Originalsprog | Engelsk |
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Tidsskrift | Journal of the London Mathematical Society |
Vol/bind | 106 |
Udgave nummer | 3 |
Sider (fra-til) | 2696-2729 |
ISSN | 0024-6107 |
DOI | |
Status | Udgivet - 2022 |
Bibliografisk note
Funding Information:
We are grateful to the anonymous referees for their many insightful comments and useful suggestions. The research of Asbjørn C. Nordentoft and Morten S. Risager was supported by the Grant DFF‐7014‐00060B from Independent Research Fund Denmark.
Publisher Copyright:
© 2022 The Authors. Journal of the London Mathematical Society is copyright © London Mathematical Society.
ID: 318802148