Polynomial parametrization for the solutions of Diophantine equations and arithmetic groups

Leonid Vaserstein

doi:10.4007/annals.2010.171.979

Polynomial parametrization for the solutions of Diophantine equations and arithmetic groups

Leonid Vaserstein

Mathematics

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

6 Scopus citations

Abstract

A polynomial parametrization for the group of integer two-by-two matrices with determinant one is given, solving an old open problem of Skolem and Beurkers. It follows that, for many Diophantine equations, the integer solutions and the primitive solutions admit polynomial parametrizations.

Original language	English (US)
Pages (from-to)	979-1009
Number of pages	31
Journal	Annals of Mathematics
Volume	171
Issue number	2
DOIs	https://doi.org/10.4007/annals.2010.171.979
State	Published - 2010

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.4007/annals.2010.171.979

Fingerprint Dive into the research topics of 'Polynomial parametrization for the solutions of Diophantine equations and arithmetic groups'. Together they form a unique fingerprint.

Cite this

@article{ed3d99fa3a884fafa6162c1f98897e50,

title = "Polynomial parametrization for the solutions of Diophantine equations and arithmetic groups",

abstract = "A polynomial parametrization for the group of integer two-by-two matrices with determinant one is given, solving an old open problem of Skolem and Beurkers. It follows that, for many Diophantine equations, the integer solutions and the primitive solutions admit polynomial parametrizations.",

author = "Leonid Vaserstein",

year = "2010",

doi = "10.4007/annals.2010.171.979",

language = "English (US)",

volume = "171",

pages = "979--1009",

journal = "Annals of Mathematics",

issn = "0003-486X",

publisher = "Princeton University Press",

number = "2",

}

TY - JOUR

T1 - Polynomial parametrization for the solutions of Diophantine equations and arithmetic groups

AU - Vaserstein, Leonid

PY - 2010

Y1 - 2010

N2 - A polynomial parametrization for the group of integer two-by-two matrices with determinant one is given, solving an old open problem of Skolem and Beurkers. It follows that, for many Diophantine equations, the integer solutions and the primitive solutions admit polynomial parametrizations.

AB - A polynomial parametrization for the group of integer two-by-two matrices with determinant one is given, solving an old open problem of Skolem and Beurkers. It follows that, for many Diophantine equations, the integer solutions and the primitive solutions admit polynomial parametrizations.

UR - http://www.scopus.com/inward/record.url?scp=77954152608&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954152608&partnerID=8YFLogxK

U2 - 10.4007/annals.2010.171.979

DO - 10.4007/annals.2010.171.979

M3 - Article

AN - SCOPUS:77954152608

VL - 171

SP - 979

EP - 1009

JO - Annals of Mathematics

JF - Annals of Mathematics

SN - 0003-486X

IS - 2

ER -