Vol. 110, No. 1, 1984

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An algorithm in a complex field and its application to the calculation of units

Malvina Florica Baica

Vol. 110 (1984), No. 1, 21–40

In the present paper the author develops a new periodic algorithm for certain algebraic number fields and calculates units in these fields from its periodicity. This algorithm (abbr. ACF) is a modification of the Jacobi-Perron Algorithm, where for the first time the expanding of the complex (not only real) numbers was possible. The ACF discloses new units of which the already known ones are special cases, and it has the advantage that many results in the theory of units can be derived by means of a unified periodic algorithm.

Mathematical Subject Classification 2000
Primary: 11R27
Secondary: 11Y40
Received: 23 February 1982
Revised: 27 August 1982
Published: 1 January 1984
Malvina Florica Baica