Polynomial parametrization for the solutions of Diophantine equations and arithmetic groups
Annals of mathematics, Tome 171 (2010) no. 2, pp. 979-1009
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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.
@article{10_4007_annals_2010_171_979,
author = {Leonid Vaserstein},
title = {Polynomial parametrization for the solutions of {Diophantine} equations and arithmetic groups},
journal = {Annals of mathematics},
pages = {979--1009},
publisher = {mathdoc},
volume = {171},
number = {2},
year = {2010},
doi = {10.4007/annals.2010.171.979},
mrnumber = {2630059},
zbl = {1221.11082},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.171.979/}
}
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Leonid Vaserstein. Polynomial parametrization for the solutions of Diophantine equations and arithmetic groups. Annals of mathematics, Tome 171 (2010) no. 2, pp. 979-1009. doi: 10.4007/annals.2010.171.979
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