✦ LIBER ✦
On Demjanenko's Matrix and Maillet's Determinant for Imaginary Abelian Number Fields
✍ Scribed by Hirofumi Tsumura
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 316 KB
- Volume
- 60
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
✦ Synopsis
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 application, we give an upper bound for the relative class number of any imaginary subfield of Q(`2m).