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Mathematics of Computation

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Quadratic extensions of totally real quintic fields

Author: Schehrazad Selmane
Journal: Math. Comp. 70 (2001), 837-843
MSC (2000): Primary 11R99, 11Y40, 11R09, 11R11, 11R29
Published electronically: March 2, 2000
MathSciNet review: 1697649
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Abstract: In this work, we establish lists for each signature of tenth degree number fields containing a totally real quintic subfield and of discriminant less than $10^{13}$ in absolute value. For each field in the list we give its discriminant, the discriminant of its subfield, a relative polynomial generating the field over one of its subfields, the corresponding polynomial over $\mathbb {Q}$, and the Galois group of its Galois closure. We have examined the existence of several non-isomorphic fields with the same discriminants, and also the existence of unramified extensions and cyclic extensions.

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Additional Information

Schehrazad Selmane
Affiliation: University of Sciences and Technology, H.B. Institute of Mathematics, B.P. 32 El Alia, Bab-Ezzouar, 16111, Algiers, Algeria

Keywords: Quintic fields, relative extensions, discriminant
Received by editor(s): March 26, 1998
Received by editor(s) in revised form: April 27, 1999
Published electronically: March 2, 2000
Article copyright: © Copyright 2000 American Mathematical Society