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Units and periodic Jacobi-Perron algorithms in real algebraic number fields of degree $3$

1975
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Transactions of the American Mathematical Society
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It is not known whether or not the Jacobi-Perron Algorithm of a vector in Rn_x, n > 3, whose components are algebraic irrationals, always becomes periodic. The author enumerates, from his previous papers, a few infinite classes of real algebraic number fields of any degree for which this is the case. Periodic Jacobi-Perron Algorithms are important, because they can be applied, inter alia, to calculate units in the corresponding algebraic number fields. The main result of this paper is expressed

doi:10.1090/s0002-9947-1975-0376504-7
fatcat:tkejwga7dbd43gctn7teq4qita