JP Journal of Algebra, Number Theory and Applications
Volume 6, Issue 2, Pages 425 - 434
(August 2006)
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SOLVING EXPLICITLY DECOMPOSABLE FORM EQUATIONS OVER GLOBAL FUNCTION FIELDS
IstvᮠGaᬠ(Hungary)
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Abstract: In [I. Gaᬠand M. Pohst, Diophantine equations over global function fields I: The Thue equation, J. Number Theory, to appear] and [I. Gaᬠand M. Pohst, Diophantine equations over global function fields II: R-integral solutions of Thue equations, J. Experimental Math., to appear] we considered Thue equations over function fields of finite characteristics. Using the fundamental lemma proved in [I. Gaᬠand M. Pohst, Diophantine equations over global function fields I: The Thue equation, J. Number Theory, to appear], the improvements of [I. Gaᬠand M. Pohst, Diophantine equations over global function fields II: R-integral solutions of Thue equations, J. Experimental Math., to appear] and the formerly known construction of Gy?ont> ry [Acta Math. Hung. 42(1-2) (1983), 45-80], in the present paper we develop a fast algorithm for solving wide classes of decomposable form equations. Our method is directly applicable for general discriminant form and index form equations, Thue equations and for certain classes of norm form equations. We illustrate our method by solving explicitly a specific equation. |
Keywords and phrases: decomposable form equations, global function fields. |
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