Polynomial parametrization for the solutions of Diophantine equations and arithmetic groups

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.

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Annals of mathematics 2010-03, Vol.171 (2), p.979-1009
1. Verfasser:	Vaserstein, Leonid
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Arithmetic Coefficients Determinants Diophantine equation Exact sciences and technology General mathematics General, history and biography Integers Mathematical congruence Mathematical rings Mathematics Number theory Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Polynomials Sciences and techniques of general use
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	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.
ISSN:	0003-486X 1939-8980
DOI:	10.4007/annals.2010.171.979