Explicit Formulae for Values of Dedekind Zeta Functions of Two Kinds of Cyclotomic Fields

作     者：马连荣 张贤科 

作者机构：Dept. of Math. Sciences Tsinghua Univ. 北京 100084 

出 版 物：《数学进展》 (Advances in Mathematics（China）)

年 卷 期：2002年第31卷第1期

页      面：90-92页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Project supported by the National Natural Science Foundation of hina (No. 10071041) 

主　　题：Dedekindζ函数 值 显式公式 Zeta函数 割圆域 

摘      要：Let K = Q(ζ_m) denote the m-th cyclotomic field, and K~+ its maximal real subfield, where ζ_m = exp(2πi/m) is an m-th primary root of unity. Let ζ_K(s) denote the Dedekind zeta function of K. For prime integers m = p, Fumio Hazama recently in [1] obtained formulae for calculating special values of ζ_K(s) and ζ_K + (s), i.e., calculating formulae of ζ_K + (1 - n) and ζ_K(1-n)/ζ_K + (1 - n) for positive integers n, which are the newest results of a series of his work in many years (see [1-3]).