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A note on Cusick's theorem on units in totally real cubic fields

Published online by Cambridge University Press:  24 October 2008

H. J. Godwin
H. J. Godwin
Affiliation:
Department of Statistics and Computer Science, Royal Holloway College, Egham, Surrey, TW20 0EX
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Extract

Let ε = ε1, with conjugates ε2, ε3, be a unit in a totally real cubic field, and let . Let ε be a unit for which T (ε) is least and let η be a unit, not a power of ε, for which T(η) is least. It was shown by Cusick[l] that ε,η form a pair of fundamental units under certain conditions. The purpose of the present note is to show that these conditions are unnecessary and that ε, η form a pair of fundamental units in all cases.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 1 , January 1984 , pp. 1 - 2
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

[1] Cusick, T. W.. Finding fundamental units in cubic fields. Math. Proc. Cambridge Philos. Soc. 92 (1982), 385–389.CrossRefGoogle Scholar
[2] Godwin, H. J.. The determination of units in totally real cubic fields. Proc. Cambridge Philos. Soc. 56 (1960), 318–321.CrossRefGoogle Scholar