Some applications of decomposable form equations to resultant equations

K. Győry

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K. Győry (1992)

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Factoring polynomials over global fields

Karim Belabas, Mark van Hoeij, Jürgen Klüners, Allan Steel (2009)

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Bernard de Mathan (1992)

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The use of D-modules to study exponential polynomials

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Thomas’ conjecture over function fields

Volker Ziegler (2007)

Journal de Théorie des Nombres de Bordeaux

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Thomas’ conjecture is, given monic polynomials $p_{1},$ $..., p_{d} \in ℤ [a]$ with $0 < deg p_{1} < \dots < deg p_{d}$ , then the Thue equation (over the rational integers) $(X - p_{1} (a) Y) \dots (X - p_{d} (a) Y) + Y^{d} = 1$ has only trivial solutions, provided $a \geq a_{0}$ 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 $d = 3$ .