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The determination of the class-numbers of totally real cubic fields

Published online by Cambridge University Press:  24 October 2008

H. J. Godwin
H. J. Godwin
Affiliation:
University College of Swansea
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Extract

In a previous paper (2) it was shown how the work of finding the units of a totally real cubic field could be facilitated by consideration of the sum of squares of differences between a number and its conjugates. In the present paper it is shown that the same ideas can be helpful in the calculation of class-numbers, and a list of the fields with class-number greater than unity and discriminant less than 20,000 is given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 4 , October 1961 , pp. 728 - 730
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

REFERENCES

(1)Davenport, H., Proc. London Math. Soc. (2), 44 (1938), 412–31.CrossRefGoogle Scholar
(2)Godwin, H. J., Proc. Cambridge Philos. Soc. 56 (1960), 318–21.CrossRefGoogle Scholar
(3)Godwin, H. J. and Samet, P. A., J. London Math. Soc. 34 (1959), 108–10.CrossRefGoogle Scholar
(4)Minkowski, H., Gesammelte Abhandiungen, Bd. I (Leipzig, 1911).Google Scholar