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Tenth degree number fields with quintic fields having one real place

Author: Schehrazad Selmane
Journal: Math. Comp. 70 (2001), 845-851
MSC (2000): Primary 11R11, 11R29, 11Y40
Published electronically: July 13, 2000
MathSciNet review: 1709158
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Abstract: In this paper, we enumerate all number fields of degree $10$ of discriminant smaller than $10^{11}$ in absolute value containing a quintic field having one real place. For each one of the $21509$ (resp. $18167)$ found fields of signature $(0,5)$ (resp. $(2,4))$ the field discriminant, the quintic field discriminant, a polynomial defining the relative quadratic extension, the corresponding relative discriminant, the corresponding polynomial over $\mathbb {Q}$, and the Galois group of the Galois closure are given. In a supplementary section, we give the first coincidence of discriminant of $19$ (resp. $20)$ nonisomorphic fields of signature $(0,5)$ (resp. $(2,4))$.

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Additional Information

Schehrazad Selmane
Affiliation: University of Sciences and Technology (U.S.T.H.B), Institut of Mathematics, B.P. 32 El Alia, Bab-Ezzouar, 16111, Algiers, Algeria

Keywords: Quintic fields, relative quadratic extensions, discriminant
Received by editor(s): November 3, 1998
Received by editor(s) in revised form: April 27, 1999
Published electronically: July 13, 2000
Article copyright: © Copyright 2000 American Mathematical Society