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On a problem of Favard concerning algebraic integers

Published online by Cambridge University Press:  17 April 2009

C. W. Lloyd-Smith
C. W. Lloyd-Smith
Affiliation:
Australian Bureau of Statistics, Post Office Box 10, Belconnen, A.C.T., 2616, Australia.
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Abstract

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Let α be an algebraic integer of degree n > 1 with conjugates α = α1, α2, …, αn. Let D(α) denote the diameter of {α1, …, αn} and diam . In 1929 Favard showed that diam and that, when n = 2 or 3, the minimal values of diam (α) are less than 2. The author shows that diam and He also finds all algebraic integers a with diam (α) ≤ 2 when n ≤ 5. Similar results are found for D(α) and, in particular, D(α) > 2 when n = 5.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 30 , Issue 1 , August 1984 , pp. 111 - 121
Copyright
Copyright © Australian Mathematical Society 1984

References

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