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
DOI:
https://doi.org/10.1090/S0025-5718-00-01210-2
Published electronically:
March 2, 2000
MathSciNet review:
1697649
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Abstract | References | Similar Articles | Additional Information
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
Email:
selmane@ist.cerist.dz
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