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arXiv · 1803.01739

On particular families of hyperquadratic continued fractions in power series fields of odd characteristic

Alain Lasjaunias
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Abstract

We discuss the form of certain algebraic continued fractions in the field of power series over $F_p$, where p is an odd prime number. This leads to give explicit continued fractions in these fields, satisfying an explicit algebraic equation of arbitrary degree $d\geq 2$ and having an irrationality measure equal to $d$. Our results are based on a mysterious finite sequence of rational numbers.

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Alain Lasjaunias. 2018-03-05. On particular families of hyperquadratic continued fractions in power series fields of odd characteristic. https://arxiv.org/abs/1803.01739

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