Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2016; 53(3): 699-709

Printed May 31, 2016

https://doi.org/10.4134/BKMS.b150240

Copyright © The Korean Mathematical Society.

Continued fraction and Diophantine equation

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