Polynomial parametrization for the solutions of Diophantine equations and arithmetic groups

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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 languageEnglish (US)
Pages (from-to)979-1009
Number of pages31
JournalAnnals of Mathematics
Volume171
Issue number2
DOIs
StatePublished - 2010

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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