Markoff triples and strong approximation

Jean Bourgain; Alexander Gamburd; Peter Sarnak

doi:10.1016/j.crma.2015.12.006

Markoff triples and strong approximation

Jean Bourgain, Alexander Gamburd, Peter Sarnak

Mathematics

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

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- 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 language	English (US)
Pages (from-to)	131-135
Number of pages	5
Journal	Comptes Rendus Mathematique
Volume	354
Issue number	2
DOIs	https://doi.org/10.1016/j.crma.2015.12.006
State	Published - Feb 1 2016

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1016/j.crma.2015.12.006

Cite this

@article{f37135235017456f8d95412436402ada,

title = "Markoff triples and strong approximation",

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- 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.",

author = "Jean Bourgain and Alexander Gamburd and Peter Sarnak",

note = "Publisher Copyright: {\textcopyright} 2016 Published by Elsevier Masson SAS on behalf of Acad{\'e}mie des sciences.",

year = "2016",

month = feb,

day = "1",

doi = "10.1016/j.crma.2015.12.006",

language = "English (US)",

volume = "354",

pages = "131--135",

journal = "Comptes Rendus Mathematique",

issn = "1631-073X",

publisher = "Academie des sciences",

number = "2",

}

TY - JOUR

T1 - Markoff triples and strong approximation

AU - Bourgain, Jean

AU - Gamburd, Alexander

AU - Sarnak, Peter

PY - 2016/2/1

Y1 - 2016/2/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84956961902&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84956961902&partnerID=8YFLogxK

U2 - 10.1016/j.crma.2015.12.006

DO - 10.1016/j.crma.2015.12.006

M3 - Article

AN - SCOPUS:84956961902

SN - 1631-073X

VL - 354

SP - 131

EP - 135

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 2

ER -

Markoff triples and strong approximation

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this