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Diophantine equations over global function fields. II: \(R\)-integral solutions of Thue equations. (English) Zbl 1142.11019

In this paper, the authors use a new method to improve the algorithm that they gave in a previous paper to solve Thue equations over global function fields. See [J. Number Theory 119, No. 1, 49–65 (2006; Zbl 1157.11011)]. The new method has two main goals. The first goal is to completely determine all solutions that can be grouped in two categories: finitely many isolated solutions and finitely many parameterized solutions that the new method helps to parameterize. The second goal of the new method is to make the algorithm more efficient than the one in the above paper. To illustrate the efficiency of the new algorithm, the authors finish the paper with two examples of Thue equations (one quartic, one cubic) over the function field \(K=k(t)\), where \(k=\mathbb{F}_5\).

MSC:

11D59 Thue-Mahler equations
11Y50 Computer solution of Diophantine equations
11R58 Arithmetic theory of algebraic function fields

Citations:

Zbl 1157.11011

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