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Markoff triples and strong approximation

Author(s): Bourgain, Jean; Gamburd, Alexander; Sarnak, Peter C

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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 (Q) over bar 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. (C) 2016 Published by Elsevier Masson SAS on behalf of Academie des sciences.
Publication Date: Feb-2016
Electronic Publication Date: 26-Jan-2016
Citation: Bourgain, Jean, Gamburd, Alexander, Sarnak, Peter. (2016). Markoff triples and strong approximation. COMPTES RENDUS MATHEMATIQUE, 354 (131 - 135. doi:10.1016/j.crma.2015.12.006
DOI: doi:10.1016/j.crma.2015.12.006
ISSN: 1631-073X
EISSN: 1778-3569
Pages: 131 - 135
Type of Material: Journal Article
Version: Author's manuscript

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