Turkish Journal of Mathematics
DOI
10.3906/mat-1303-61
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
First Page
191
Last Page
202
Recommended Citation
AYADI, KHALIL and TAKTAK, FATMA
(2014)
"On the continued fraction expansion of some hyperquadratic functions,"
Turkish Journal of Mathematics: Vol. 38:
No.
2, Article 1.
https://doi.org/10.3906/mat-1303-61
Available at:
https://journals.tubitak.gov.tr/math/vol38/iss2/1
