Effective equidistribution and property tau

Abstract

We prove a quantitative equidistribution statement for adelic homogeneous subsets whose stabilizer is maximal and semisimple. Fixing the ambient space, the statement is uniform in all parameters. We explain how this implies certain equidistribution theorems which, even in a qualitative form, are not accessible to measure-classification theorems. As another application, we describe another proof of property tau for arithmetic groups.

Final version, to appear in JAMS

References in corpus (2)

• Local-global principles for representations of quadratic forms
• Distribution of Shapes of orthogonal Lattices

Cited by in corpus (3)

• Quantitative behavior of unipotent flows and an effective avoidance principle
• Almost-primes in horospherical flows on the space of lattices
• On effective equidistribution for quotients of SL(d)