Nordentoft, Asbjorn C;
Petridis, Yiannis N;
Risager, Morten S;
(2022)
Small-scale equidistribution of Hecke eigenforms at infinity.
Journal of the London Mathematical Society
10.1112/jlms.12645.
(In press).
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Abstract
We investigate the equidistribution of Hecke eigenforms on sets that are shrinking towards infinity. 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 interesting transition behavior at half the Planck scale.
| Type: | Article |
|---|---|
| Title: | Small-scale equidistribution of Hecke eigenforms at infinity |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1112/jlms.12645 |
| Publisher version: | https://doi.org/10.1112/jlms.12645 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third-party material in this article are included in the Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ |
| Keywords: | Science & Technology, Physical Sciences, Mathematics, QUANTUM UNIQUE ERGODICITY, MASS EQUIDISTRIBUTION, EIGENFUNCTIONS, VARIANCE, BOUNDS, ZEROS, SETS |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10151386 |
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