English

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 \SL2\SL_2, as well as of the Bourgain-Gamburd argument for expansion of Cayley graphs modulo primes of subgroups of \SL2(\Zz)\SL_2(\Zz) which are Zariski-dense in \SL2\SL_2.

Keywords

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)

R2 v1 2026-06-21T20:00:39.929Z