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2006 Diophantine Equations over Global Functions Fields II: R-Integral Solutions of Thue Equations
IstvÁn GaÁl, Michael Pohst
Experiment. Math. 15(1): 1-6 (2006).

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.

Citation

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IstvÁn GaÁl. Michael Pohst. "Diophantine Equations over Global Functions Fields II: R-Integral Solutions of Thue Equations." Experiment. Math. 15 (1) 1 - 6, 2006.

Information

Published: 2006
First available in Project Euclid: 16 June 2006

zbMATH: 1142.11019
MathSciNet: MR2229380

Subjects:
Primary: 11D59 , 11R58 , 11Y50

Keywords: global function fields , Thue equations

Rights: Copyright © 2006 A K Peters, Ltd.

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