A Uniform Strong Spectral Gap for Congruence Covers of a compact quotient of PSL(2,R)^d

Details A Uniform Strong Spectral Gap for Congruence Covers of a compact quotient of PSL(2,R)^d A Uniform Strong Spectral Gap for Congruence Covers of a compact quotient of PSL(2,R)^d

2010-02-18

arxiv.org/abs/1002.3422v2

Mathematics

Number Theory

22 pages, Order and numbering of theorems has changed. Final version, to appear in IMRN

Scientific paper

The existence of a strong spectral gap for lattices in semi-simple Lie groups is crucial in many applications. In particular, for arithmetic lattices it is useful to have bounds for the strong spectral gap that are uniform in the family of congruence covers. When the lattice is itself a congruence group, there are uniform and very good bounds for the spectral gap coming from the known bounds toward the Ramanujan-Selberg conjectures. In this note, we establish a uniform bound for the strong spectral gap for congruence covers of an irreducible co-compact lattice $\Gamma$ in $PSL(2,R)^d$ with $d\geq 2$, which is the simplest and most basic case where the congruence subgroup property is not known.

Affiliated with

Also associated with

No associations

Rating

A Uniform Strong Spectral Gap for Congruence Covers of a compact quotient of PSL(2,R)^d does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Uniform Strong Spectral Gap for Congruence Covers of a compact quotient of PSL(2,R)^d, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Uniform Strong Spectral Gap for Congruence Covers of a compact quotient of PSL(2,R)^d will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-404744