Vol. 81, No. 2, 1979

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A class of fundamental units and some classes of Jacobi-Perron algorithms in pure cubic fields

Claude Levesque

Vol. 81 (1979), No. 2, 447–466

In this paper, we consider some pure cubic fields of the form K = Q((D3 ± d)13) where D,d N and d3D2. Under certain conditions, we obtain the fundamental unit η of K by ruling out the case where η is the square of a unit. We also give three new classes of vectors, whose Jacobi-Perron Algorithms are periodic. The first ten vectors of a generalized Jacobi-Perron Algorithm are then written down. A generalization of the Bernstein formula is also achieved.

Mathematical Subject Classification
Primary: 12A45, 12A45
Secondary: 12A30
Received: 8 December 1975
Revised: 15 February 1978
Published: 1 April 1979
Claude Levesque