Class number formulae in the form of a product of determinants in function fields
Class number formulae in the form of a product of determinants in function fields
复制标题
函数域行列式乘积形式的类数公式
DOI：
10.1017/s1446788700008053
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发表时间：
2005
影响因子：
0.7
通讯作者：
H. Jung
中科院分区：
文献类型：
--
作者：
Jaehyun Ahn;S. Choi;H. Jung
本文推广Kuč时代的群行列式公式，以行列式乘积的形式得到任意导体分圆函数域的任意子域的实类数公式和相对类数公式。根据这些公式，推广了Rosen和Bae-Kang的相对类数公式，得到了TSumura和Hirabayashi关于素幂导体割圆函数塔中中间场的类似结果。
Abstract In this paper, we generalize the Kučera's group-determinant formulae to obtain the real and relative class number formulae of any subfield of cyclotomic function fields with arbitrary conductor in the form of a product of determinants. From these formulae, we generalize the relative class number formula of Rosen and Bae-Kang and obtain analogous results of Tsumura and Hirabayashi for an intermediate field in the tower of cyclotomic function fields with prime power conductor.