On the continued fraction expansion of some hyperquadratic functions

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

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 a satisfying an equation a = f(ar), 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.

Anahtar Kelimeler:

Finite fields, formal power series, continued fraction

On the continued fraction expansion of some hyperquadratic functions

Keywords:

Finite fields, formal power series, continued fraction,

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