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Journal of the London Mathematical Society 1988 s2-38(1):33-46; doi:10.1112/jlms/s2-38.1.33
© 1988 by London Mathematical Society
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© Oxford University Press

Discriminant Minimal Et Petits Discriminants Des Corps De Nombres De Degre 7 Avec Cinq Places Reelles

F. Diaz Y Diaz

Université de Paris-Sud, Mathématiques Bâat. 425, 91405 Orsay Cedex, France

In this paper we give a list of degree-7 number fields having five real places whose discriminant is smaller than 5000000 in absolute value. This list contains all the number fields having a discriminant which is, in absolute value, smaller than 3477288. We also conjecture that the list actually contains all the number fields with discriminants whose absolute value is smaller than 4467575.

The minimal discriminant for these types of number fields is –2306599. This result puts an end to the problem of determining the minimal discriminants for the degree-7 number fields.


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