25 research outputs found
On hyperquadratic continued fractions in power series fields over a finite field
The first part of this note is a short introduction on continued fraction
expansions for certain algebraic power series. In the last part, as an
illustration, we present a family of algebraic continued fractions of degree 4,
including a toy example considered about thirty years ago in a pioneer work in
this area
On certain recurrent and automatic sequences in finite fields
In this work we extend our study on a link between automaticity and certain
algebraic power series over finite fields. Our starting point is a family of
sequences in a finite field of characteristic , recently introduced by the
first author in connection with algebraic continued fractions. By including it
in a large family of recurrent sequences in an arbitrary finite field, we prove
its automaticity. Then we give a criterion on automatic sequences, generalizing
a previous result and this allows us to present new families of automatic
sequences in an arbitrary finite field.Comment: 10 page
Hyperquadratic continued fractions over a finite field of odd characteristic with partial quotients of degree 1
In 1986, some examples of algebraic, and nonquadratic, power series over a
finite prime field, having a continued fraction expansion with partial
quotients all of degree one, were discovered by W. Mills and D. Robbins. In
this note we show how these few examples are included in a very large family of
continued fractions for certain algebraic power series over an arbitrary finite
field of odd characteristic