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The minimum discriminants of quintic fields

Published online by Cambridge University Press:  18 May 2009

John Hunter
John Hunter
Affiliation:
The University Glasgow
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Let D be the discriminant of an algebraic number field F of degree n over the rational field R. The problem of finding the lowest absolute value of D as F varies over all fields of degree n with a given number of real (and consequently of imaginary) conjugate fields has not yet been solved in general. The only precise results so far given are those for n = 2, 3 and 4. The case n = 2 is trivial; n = 3 was solved in 1896 by Furtwangler, and n = 4 in 1929 by J. Mayer [6]. Reference to Furtwangler's work is given hi Mayer's paper. In this paper the results for n = 5, that is, for quintic fields, are obtained.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 3 , Issue 2 , June 1957 , pp. 57 - 67
Copyright
Copyright © Glasgow Mathematical Journal Trust 1957

References

REFERENCES

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6.Mayer, J., Die absolut-kleinsten Diskriminanten der biquadratischen Zahlkörper, S.-B. Akad. Wiss. Wien Abt. Ila. 138 (1929), 733–742.Google Scholar