Quantum Unique Ergodicity for Locally Symmetric Spaces Ii

Content Provider	Semantic Scholar
Author	Silberman, Lior Venkatesh, Akshay
Copyright Year	2006
Abstract	We prove the arithmetic quantum unique ergodicity (AQUE) conjecture for non-degenerate sequences of Hecke eigenfunctions on quotients Γ\G/K, where G ' PGLd(R), K is a maximal compact subgroup of G and Γ < G is a lattice associated to a division algebra over Q of prime degree d. The primary novelty of the present paper is a new method of proving positive entropy of quantum limits, which avoids sieves and yields better bounds than previous techniques. The result on AQUE is obtained by combining this with a measure-rigidity theorem due to Einsiedler-Katok, following a strategy first pioneered by Lindenstrauss.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://www.math.harvard.edu/~lior/work/AQUE-nov6.pdf
Alternate Webpage(s)	http://www.math.ubc.ca/~lior/work/AQUE-nov6.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article