Experimental Mathematics

Diophantine Equations over Global Functions Fields II: R-Integral Solutions of Thue Equations

IstvÁn GaÁl and Michael Pohst

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Abstract

Let {\small $K$} be an algebraic function field over a finite field. Let {\small $L$} be an extension field of {\small $K$} of degree at least 3. Let {\small $R$} be a finite set of valuationsof {\small $K$} and denote by {\small $S$} the set of extensions of valuations of {\small $R$} to {\small $L$}. Denote by {\small $O_{K,R},O_{L,S}$} the ring of {\small $R$}-integers of {\small $K$} and {\small $S$}-integers of {\small $L$}, respectively. Assume that {\small $\alpha\in O_{L,S}$} with {\small $L=K(\alpha)$}, let {\small $0\neq \mu\in O_{K,R}$}, and consider the solutions {\small $(x,y)\in O_{K,R}$} of the Thue equation

{\small \[ N_{L/K}(x-\alpha y)=\mu.\]}

We give an efficient method for calculating the {\small $R$}-integral solutions of the above equation. The method is different from that in our previous paper and is much more efficient in many cases.

Article information

Source
Experiment. Math., Volume 15, Number 1 (2006), 1-6.

Dates
First available in Project Euclid: 16 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.em/1150476898

Mathematical Reviews number (MathSciNet)
MR2229380

Zentralblatt MATH identifier
1142.11019

Subjects
Primary: 11D59: Thue-Mahler equations 11Y50: Computer solution of Diophantine equations 11R58: Arithmetic theory of algebraic function fields [See also 14-XX]

Keywords
Thue equations global function fields

Citation

GaÁl, IstvÁn; Pohst, Michael. Diophantine Equations over Global Functions Fields II: R-Integral Solutions of Thue Equations. Experiment. Math. 15 (2006), no. 1, 1--6. https://projecteuclid.org/euclid.em/1150476898


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