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Quantum unique ergodicity on locally symmetric spaces: the degenerate lift
| Content Provider | Semantic Scholar |
|---|---|
| Author | Silberman, Lior |
| Copyright Year | 2011 |
| Abstract | Given a measure $\bar\mu$ on a locally symmetric space $Y=\Gamma\backslash G/K$, obtained as a weak-{*} limit of probability measures associated to eigenfunctions of the ring of invariant differential operators, we construct a measure $\mu$ on the homogeneous space $X=\Gamma\backslash G$ which lifts $\bar\mu$ and which is invariant by a connected subgroup $A_{1}\subset A$ of positive dimension, where $G=NAK$ is an Iwasawa decomposition. If the functions are, in addition, eigenfunctions of the Hecke operators, then $\mu$ is also the limit of measures associated to Hecke eigenfunctions on $X$. This generalizes previous results of the author and A.\ Venkatesh to the case of "degenerate" limiting spectral parameters. |
| Starting Page | 632 |
| Ending Page | 650 |
| Page Count | 19 |
| File Format | PDF HTM / HTML |
| DOI | 10.4153/cmb-2015-023-0 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1104.0074v1.pdf |
| Alternate Webpage(s) | https://cms.math.ca/cmb/abstract/pdf/151290.pdf |
| Alternate Webpage(s) | https://doi.org/10.4153/cmb-2015-023-0 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
