Invariant measures and arithmetic quantum unique ergodicity

Elon Lindenstrauss*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

192 Scopus citations


We classify measures on the locally homogeneous space Γ\ SL(2, ℝ) × L which are invariant and have positive entropy under the diagonal subgroup of SL(2, ℝ) and recurrent under L. This classification can be used to show arithmetic quantum unique ergodicity for compact arithmetic surfaces, and a similar but slightly weaker result for the finite volume case. Other applications are also presented. In the appendix, joint with D. Rudolph, we present a maximal ergodic theorem, related to a theorem of Hurewicz, which is used in theproof of the main result.

Original languageAmerican English
Pages (from-to)165-219
Number of pages55
JournalAnnals of Mathematics
Issue number1
StatePublished - 2006
Externally publishedYes


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