On Demjanenko's Matrix and Maillet's Determinant for Imaginary Abelian Number Fields
On Demjanenko's Matrix and Maillet's Determinant for Imaginary Abelian Number Fields
复制标题
论虚数阿贝尔数域的 Demjanenko 矩阵和 Maillet 行列式
DOI：
10.1006/jnth.1996.0113
复制
发表时间：
1996
影响因子：
0.7
通讯作者：
Hirofumi Tsumura
中科院分区：
文献类型：
--
作者：
Hirofumi Tsumura
构造了任意虚阿贝尔域的Demjanenko矩阵的推广，并证明了该矩阵的行列式与相对类数之间的关系公式。在特殊情况下，我们证明了这个矩阵的行列式与梅勒行列式重合。作为一个应用，我们给出了Q （ζ 2m）的任意虚子域的相对类数的上界。
Abstract 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 ( ζ 2 m ).