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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
Email: sc_selmane@hotmail.com

DOI: http://dx.doi.org/10.1090/S0025-5718-00-01232-1
PII: S 0025-5718(00)01232-1
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