Hyperquadratic continued fractions over a finite field of odd characteristic with partial quotients of degree 1

2014/05/09 by Lasjaunias, Alain, Yao, Jia-Yan
#11J70 #11T55 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1405.2171

Abstract

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.

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