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Volker Ziegler
Thomas’ conjecture over function fields
Journal de théorie des nombres de Bordeaux, 19 no. 1 (2007), p. 289-309, doi: 10.5802/jtnb.587
Article PDF | Reviews Zbl pre05186988
Keywords: Thue equation, function fields

Résumé - Abstract

Thomas’ conjecture is, given monic polynomials $p_1,$ $\ldots ,p_d \in \mathbb{Z}[a]$ with $0<\deg p_1< \cdots <\deg p_d$, then the Thue equation (over the rational integers)

$$(X-p_1(a) Y) \cdots (X-p_d(a) Y)+ Y^d=1$$

has only trivial solutions, provided $a\ge a_0$ with effective computable $a_0$. We consider a function field analogue of Thomas’ conjecture in case of degree $d=3$. Moreover we find a counterexample to Thomas’ conjecture for $d=3$.

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