Families of periodic Jacobi-Perron algorithms for all period lengths

Abstract

For all integers $m\ge n\ge 2$, 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.

like published version, incorporates referee's changes as well as other improvements

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