Explicit growth and expansion for SL_2
Number Theory
2012-07-03 v3 Group Theory
Abstract
We give explicit versions of Helfgott's Growth Theorem for , as well as of the Bourgain-Gamburd argument for expansion of Cayley graphs modulo primes of subgroups of which are Zariski-dense in .
Cite
@article{arxiv.1201.1139,
title = {Explicit growth and expansion for SL_2},
author = {Emmanuel Kowalski},
journal= {arXiv preprint arXiv:1201.1139},
year = {2012}
}
Comments
42 pages; v3, major corrections, including (almost) all numerical constants, and correction of one serious mistake, giving much worse expansion bounds (many thanks to the referee for this paper)