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arXiv · 1505.04721

Families of periodic Jacobi-Perron algorithms for all period lengths

Paul Voutier
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Abstract

For all integers $m \geq n \geq 2$, we exhibit infinite families of purely periodic Jacobi-Perron Algorithm (JPA) expansions of dimension $n$ with period length equal to $m$ along with the associated Hasse-Bernstein units. Some observations on the units of Levesque-Rhin as well as the periodicity of the JPA expansion of $\left( m^{1/3}, m^{2/3} \right)$ are also made.

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Paul Voutier. 2016-07-03. Families of periodic Jacobi-Perron algorithms for all period lengths. https://doi.org/10.1016/j.jnt.2016.04.003

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