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

Alain Lasjaunias; Jia-Yan Yao

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arXiv · 1405.2171

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

Alain Lasjaunias·Jia-Yan Yao

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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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Alain Lasjaunias, Jia-Yan Yao. 2014-05-09. Hyperquadratic continued fractions over a finite field of odd characteristic with partial quotients of degree 1. https://arxiv.org/abs/1405.2171

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