Abstract
We study joint quasimodes of the Laplacian and one Hecke operator on compact congruence surfaces, and give conditions on the orders of the quasimodes that guarantee positive entropy on almost every ergodic component of the corresponding semiclassical measures. Together with the measure classification result of (Lindenstrauss, Ann Math (2) 163(1):165–219, 2006), this implies Quantum Unique Ergodicity for such functions. Our result is optimal with respect to the dimension of the space from which the quasi-mode is constructed. We also study equidistribution for sequences of joint quasimodes of the two partial Laplacians on compact irreducible quotients of (formula presented).
| Original language | English |
|---|---|
| Pages (from-to) | 219-259 |
| Number of pages | 41 |
| Journal | Inventiones Mathematicae |
| Volume | 198 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Oct 2014 |
Bibliographical note
Publisher Copyright:© 2014, Springer-Verlag Berlin Heidelberg.
Funding
S. Brooks was partially supported by NSF grant DMS-1101596. E. Lindenstrauss was supported by the ERC (AdG Grant 267259), NSF grant DMS-0800345, and ISF grant 983/09.
| Funders | Funder number |
|---|---|
| Israel Science Foundation | |
| National Stroke Foundation | |
| National Science Foundation | DMS-1101596 |
| Directorate for Mathematical and Physical Sciences | 0800345, 1101596 |
| European Commission | 267259, DMS-0800345 |
| Israel Science Foundation | 983/09 |