Markoff triples and strong approximation

被引：20
|
作者：
Bourgain, Jean [1 ]
Gamburd, Alexander [2 ]
Sarnak, Peter [1 ,3 ]
机构：
[1] IAS, San Francisco, CA 94104 USA
[2] CUNY, Grad Ctr, New York, NY 10017 USA
[3] Princeton Univ, Princeton, NJ 08544 USA
来源：
COMPTES RENDUS MATHEMATIQUE | 2016年 / 354卷 / 02期
基金：
美国国家科学基金会;
关键词：
VARIETIES; NUMBERS; POINTS;
D O I：
10.1016/j.crma.2015.12.006
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：131 / 135
页数：5
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