On the continued fraction expansion of some hyperquadratic functions

Authors: KHALIL AYADI, FATMA TAKTAK

Abstract: In this paper, we consider continued fraction expansions for algebraic power series over a finite field. Especially, we are interested in studying the continued fraction expansion of a particular subset of algebraic power series over a finite field, called hyperquadratic. This subset contains irrational elements \alpha satisfying an equation \alpha = f(\alpha^r), where r is a power of the characteristic of the base field and f is a linear fractional transformation with polynomials coefficients. The continued fraction expansion for these elements can sometimes be given fully explicitly. We will show this expansion for hyperquadratic power series satisfying certain types of equations.

Keywords: Finite fields, formal power series, continued fraction

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