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Remarks on unit indices of imaginary abelian number fields

✍ Scribed by Mikihito Hirabayashi; Ken-ichi Yoshino

Book ID
105137565
Publisher
Springer
Year
1988
Tongue
English
Weight
440 KB
Volume
60
Category
Article
ISSN
0025-2611

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πŸ“œ SIMILAR VOLUMES

On Bases of Groups of Circular Units of
On Bases of Groups of Circular Units of Some Imaginary Abelian Number Fields
✍ Kazuhiro Dohmae πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 820 KB

Let k be an imaginary abelian number field whose conductor has at most two distinct prime divisors and whose maximal subfields which are ramified at one prime are imaginary. We shall find a basis for the group C of circular units in k and compute the index of C in the group E of units in k.

On Demjanenko's Matrix and Maillet's Det
On Demjanenko's Matrix and Maillet's Determinant for Imaginary Abelian Number Fields
✍ Hirofumi Tsumura πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 316 KB

We construct a generalization of Demjanenko's matrix for an arbitrary imaginary abelian field and prove a relation formula between the determinant of this matrix and the relative class number. In a special case, we prove that the determinant of this matrix coincides with Maillet's determinant. As an