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 | |
| State | Published - Jul 6 2010 |
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All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
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Polynomial parametrization for the solutions of Diophantine equations and arithmetic groups. / Vaserstein, Leonid.
In: Annals of Mathematics, Vol. 171, No. 2, 06.07.2010, p. 979-1009.Research output: Contribution to journal › Article
TY - JOUR
T1 - Polynomial parametrization for the solutions of Diophantine equations and arithmetic groups
AU - Vaserstein, Leonid
PY - 2010/7/6
Y1 - 2010/7/6
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.
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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 -