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Discriminant Minimal Et Petits Discriminants Des Corps De Nombres De Degre 7 Avec Cinq Places Reelles
Author(s) -
Diaz Y Diaz F.
Publication year - 1988
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-38.1.33
Subject(s) - discriminant , mathematics , combinatorics , algebraic number field , conjecture , value (mathematics) , degree (music) , linear discriminant analysis , statistics , physics , artificial intelligence , computer science , acoustics
In this paper we give a list of degree‐7 number fields having five real places whose discriminant is smaller than 5 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.