Geodesic
The minimum discriminants of quintic fields
Glasgow mathematical journal, Tome 2 (1957) no. 2, pp. 57-67

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Hunter, John. The minimum discriminants of quintic fields. Glasgow mathematical journal, Tome 2 (1957) no. 2, pp. 57-67. doi: 10.1017/S2040618500033463
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