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Mathematics of Computation

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A table of totally real quintic number fields

Author: F. Diaz y Diaz
Journal: Math. Comp. 56 (1991), 801-808, S1
MSC: Primary 11Y40; Secondary 11R21, 11R29, 11R32
MathSciNet review: 1068820
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Abstract: We give a table of the 1077 totally real number fields of degree five having a discriminant less than 2 000 000. There are two nonisomorphic fields of discriminant 1 810 969 and two nonisomorphic fields of discriminant 1 891 377. All the other number fields in the table are characterized by their discriminant. Among these fields, three are cyclic and four have a Galois closure whose Galois group is the dihedral group $ {D_5}$. The Galois closure for all the other fields in the table has a Galois group isomorphic to $ {S_5}$.

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Keywords: Totally real number fields, discriminant, Galois group
Article copyright: © Copyright 1991 American Mathematical Society

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