Markoff triples and strong approximation

Jean Bourgain, Alexander Gamburd, Peter Sarnak

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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 Q- 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.

Original languageEnglish (US)
Pages (from-to)131-135
Number of pages5
JournalComptes Rendus Mathematique
Issue number2
StatePublished - Feb 1 2016

All Science Journal Classification (ASJC) codes

  • General Mathematics


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