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Families of periodic Jacobi--Perron algorithms in any dimension with period lengths going to infinity

Volume 177 / 2017

Brigitte Adam Acta Arithmetica 177 (2017), 293-299 MSC: Primary 11A55; Secondary 11R27. DOI: 10.4064/aa8471-8-2016 Published online: 31 January 2017


One of the generalizations of the continued fraction algorithm to higher dimensions is the Jacobi–Perron Algorithm (JPA). C. Levesque and G. Rhin obtained the JPA expansion of two parametrized infinite families of degree 3, each depending on two parameters. These expansions are purely periodic. We generalize these families to parametrized families (depending on three parameters) of fields with any degree higher than 3.


  • Brigitte Adam2, Clos du Pré
    57530 Courcelles-Chaussy, France

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