Markoff Triples and Strong Approximation
Number Theory
2015-11-05 v2
Abstract
We investigate the transitivity properties of the group of morphisms generated by Vieta involutions on the solutions in congruences to the Markoff equation as well as to other Markoff type affine cubic surfaces. These are dictated by the finite orbits of these actions and these can be determined effectively. The results are applied to give forms of strong approximation for integer points, and to sieving, on these surfaces
Cite
@article{arxiv.1505.06411,
title = {Markoff Triples and Strong Approximation},
author = {Jean Bourgain and Alex Gamburd and Peter Sarnak},
journal= {arXiv preprint arXiv:1505.06411},
year = {2015}
}