Vol. 109, No. 2, 1983

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On units of pure quartic number fields

Akira Endô

Vol. 109 (1983), No. 2, 327–333
Abstract

Let K = Q(4√D4-±-d) be a pure quartic number field, where D and d are natural numbers such that d divides D3 and d is fourth power free. Then 𝜀 = ±(4√D4-±-d + D)(√4D4--±-dD) is a unit of K whose relative norm to the quadratic subfield of K is 1. We consider the condition for 𝜀 to be a member of a system of fundamental units of K.

Mathematical Subject Classification 2000
Primary: 11R27
Secondary: 11R16
Milestones
Received: 2 April 1981
Revised: 28 April 1982
Published: 1 December 1983
Authors
Akira Endô