关于分圆域及其最大实子域的类数上界

On the Upper Bounds for Class Numbers of Cyclotomic Fields and Their Maximal Real Subfields

中文关键词:  分圆域  类数  上界

英文关键词:cyclotomic field, class number, upper bound.

中文摘要:

      设ｍ是适合m≠2（ｍｏｄ４）的整数，(?)是ｍ次本原单位根，又设Δ_k,h_m分别是分圆域Ｋ＝Ｑ(?)的判别式和类数．本文证明了：

英文摘要:

      Let m be a positive in tegers with m≠2(mod 4) , and let (?) be a prim itive m th root of unity. Let K=Q(?), and let Δ_k,h_m be the discri minant and the class number of K.