CONTINUED FRACTION AND DIOPHANTINE EQUATION

Title & Authors
CONTINUED FRACTION AND DIOPHANTINE EQUATION

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;
Language
English
Cited by
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