Periodic Jacobi-Perron algorithms and fundamental units
Nambury S. Raju · Pacific Journal of Mathematics · 1976
In this paper the author states a class of infinitely many real cubic fields for which the Jacobi-Perron algorithm of a properly chosen vector becomes periodic and calculates explicitly a fundamental unit for each field.The main results of this paper are: Let m=α 6 + 3α 3 + 3, ω = λ/m, ra cube free a EN] then the Jacobi-Perron algorithm of α (0) = (ω, ω 2 ) is periodic.The length of the primitive preperiod is four and the length of the primitive period is three.A fundamental unit in Q(ω) is given by e = α 3 + 1aω.