On the resolution of index form equations in dihedral quartic number fields

István Gaál, A. Pethő, Michael Pohst

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7 Citations (Scopus)

Abstract

We describe a new algorithm, basedon sieving procedures, for determining the minimal index and all elements with minimal index in a class of totally real quartic fields with Galois group D8. It is not universally applicable, but its applicability is easily checked for any particular example, and it is very fast when applicable. We include several tables demonstrating the potential of the method. (A more general approach for quartic fields, described in [Gaál et al.], requires much more computation time for each field.) Finally, we present a family of totally real quartic fields with Galois group D8 and having minimal index 1 (that is, a power integral basis).

Original languageEnglish
Pages (from-to)245-254
Number of pages10
JournalExperimental Mathematics
Volume3
Issue number3
DOIs
Publication statusPublished - Jan 1 1994

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Number field
Galois group
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On the resolution of index form equations in dihedral quartic number fields. / Gaál, István; Pethő, A.; Pohst, Michael.

In: Experimental Mathematics, Vol. 3, No. 3, 01.01.1994, p. 245-254.

Research output: Contribution to journalArticle

Gaál, István ; Pethő, A. ; Pohst, Michael. / On the resolution of index form equations in dihedral quartic number fields. In: Experimental Mathematics. 1994 ; Vol. 3, No. 3. pp. 245-254.
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