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math.NT2016
Entropy bounds and quantum unique ergodicity for Hecke eigenfunctions on division algebras
Lior Silberman, Akshay Venkatesh
We prove the arithmetic quantum unique ergodicity (AQUE) conjecture for non-degenerate sequences of Hecke eigenfunctions on quotients , where $G\simeq\mathrm{PGL}_…
math.NT2010
A uniform spectral gap for congruence covers of a hyperbolic manifold
Dubi Kelmer, Lior Silberman
Let be $\SO(n,1)$ or $\SU(n,1)$ and let denote an arithmetic lattice. The hyperbolic manifold $Γ\backslash \calH$ comes with a natural family of covers, coming fro…