arXiv Analytics

Sign in

arXiv:0812.0330 [math.NT]AbstractReferencesReviewsResources

Polynomial parametrization of the solutions of Diophantine equations of genus 0

Sophie Frisch, Günter Lettl

Published 2008-12-01Version 1

Let f in Z[X,Y,Z] be a non-constant, absolutely irreducible, homogeneous polynomial with integer coefficients, such that the projective curve given by f=0 has a function field isomorphic to the rational function field Q(t). We show that all integral solutions of the Diophantine equation f=0 (up to those corresponding to some singular points) can be parametrized by a single triple of integer-valued polynomials. In general, it is not possible to parametrize this set of solutions by a single triple of polynomials with integer coefficients.

Comments: Dedicated to Prof. W. Narkiewicz on the occasion of his 70th birthday. To appear in Functiones et Approximatio. 4 pages
Journal: Funct. Approx. Comment. Math. 39 (2008), part 2, 205-209
Categories: math.NT, math.AC
Subjects: 11D85, 13F20, 11D41, 14H05
Related articles: Most relevant | Search more
arXiv:1201.0730 [math.NT] (Published 2012-01-03)
On the Diophantine equation x^2+2^a.3^b.11^c=y^n
arXiv:math/0304425 [math.NT] (Published 2003-04-27)
Modular congruences, Q-curves, and the diophantine equation x^4 + y^4 = z^p
arXiv:1003.3160 [math.NT] (Published 2010-03-16)
Note on the diophantine equation X^t+Y^t=BZ^t

Links

Toolbox