The minimum discriminants of quintic fields

1 December 1956

journal article
research article
Published by Cambridge University Press (CUP) in Proceedings of the Glasgow Mathematical Association

Vol. 3 (2) , 57-67
https://doi.org/10.1017/s2040618500033463

Abstract

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.

Keywords

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A numerical study of quintics of small discriminant
Communications on Pure and Applied Mathematics, 1955