Research Article On the continued fraction expansion of some hyperquadratic functions

Abstract: In this paper, we consider continued fraction expansions for algebraic power series over a nite eld. Especially, we are interested in studying the continued fraction expansion of a particular subset of algebraic power series over a nite eld, called hyperquadratic. This subset contains irrational elements satisfying an equation = f(r), where r is a power of the characteristic of the base eld and f is a linear fractional transformation with polynomials coecients. 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. Key words: Finite elds, formal power series, continued fraction 1