Continued fraction and Diophantine equation
Bull. Korean Math. Soc. 2016 Vol. 53, No. 3, 699-709
Published online May 31, 2016
Wiem Gadri and Mohamed Mkaouar
Facult\'e des Sciences de Sfax, Facult\'e des Sciences de Sfax
Abstract : Our paper is devoted to the study of certain diophantine equations on the ring of polynomials over a finite field, which are intimately related to algebraic formal power series which have partial quotients of unbounded degree in their continued fraction expansion. In particular it is shown that there are Pisot formal power series with degree greater than 2, having infinitely many large partial quotients in their simple continued fraction expansions. This generalizes an earlier result of Baum and Sweet for algebraic formal power series.
Keywords : Pisot element, continued fraction, Laurent series in finite fields
MSC numbers : 11A55, 11D72, 11J61, 11J68
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