Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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Quadratic extensions of totally real quintic fields
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by Schehrazad Selmane;
Math. Comp. 70 (2001), 837-843
DOI: https://doi.org/10.1090/S0025-5718-00-01210-2
Published electronically: March 2, 2000

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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Bibliographic 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
  • Received by editor(s): March 26, 1998
  • Received by editor(s) in revised form: April 27, 1999
  • Published electronically: March 2, 2000
  • © Copyright 2000 American Mathematical Society
  • 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
  • MathSciNet review: 1697649