Journal Article

THOMAS'S FAMILY OF THUE EQUATIONS OVER FUNCTION FIELDS

CLEMENS FUCHS and VOLKER ZIEGLER

in The Quarterly Journal of Mathematics

Volume 57, issue 1, pages 81-91
Published in print March 2006 | ISSN: 0033-5606
Published online March 2006 | e-ISSN: 1464-3847 | DOI: http://dx.doi.org/10.1093/qmath/hah062
THOMAS'S FAMILY OF THUE EQUATIONS OVER FUNCTION FIELDS

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We consider a function field analogue of Thomas's family of Thue equations X3 − (λ − 1)X2Y − (λ + 2)X Y2 − Y3 = ξ, where the solutions X,Y come from the ring C[T], the parameter λ ∈ C[T] is some non-constant polynomial and 0 ≠ ξ ∈ C. In this paper we solve this family completely.

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Subjects: Pure Mathematics

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