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.


Leonid Vaserstein

Department of Mathematics
Penn State University
University Park, PA 16802-6401
United States