Vol. 64, No. 1, 1976

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ISSN: 0030-8730
Periodic Jacobi-Perron algorithms and fundamental units

Nambury Sitarama Raju

Vol. 64 (1976), No. 1, 241–251
Abstract

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 = a6 + 3a3 + 3, ω = √3m--, m cube free a N; then the Jacobi-Perron algorithm of a(0) = (ω,ω2) 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 = a3 + 1 .

Mathematical Subject Classification
Primary: 12A30, 12A30
Secondary: 12A45
Milestones
Received: 20 November 1975
Revised: 25 March 1976
Published: 1 May 1976
Authors
Nambury Sitarama Raju