Tenth degree number fields with quintic fields having one real place (Q2701570)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Tenth degree number fields with quintic fields having one real place |
scientific article |
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Tenth degree number fields with quintic fields having one real place (English)
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19 February 2001
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tenth degree fields
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discriminants
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quintic subfield
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subfield
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minimal polynomial
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Galois group
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tables
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The author has calculated all tenth degree number fields with discriminants smaller than \(10^{11}\) containing a quintic subfield having one real place. For the signatures (0,5) and (2,4), 21509 and 18167 fields are found, respectively. For each field the discriminant, the subfield, the minimal polynomial of its generating element (relative and absolute) and the Galois group are computed. These computations give rise to tables extending former tables for lower degree number fields. The paper is illustrated by interesting tables. Corresponding results of the author for tenth degree fields can be found in [Math. Comput. 70, 837-843 (2001; Zbl 0991.11069)].
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