AN ELEMENTARY CRITERION ON PARITY OF CLASS NUMBER OF CYCLIC NUMBER FIELD

作     者：冯克勤 FENG KEQIN University of Science and Technology of China, Hefei

作者机构：University of Science and Technology of China Hefei 

出 版 物：《Science in China,Ser.A》 (中国科学A辑(英文版))

年 卷 期：1982年第10期

页      面：1032-1041页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：CLASS calculating parity elementary criterion totally elusion generating polynomial defining 

摘      要：Let K be a subfield of cyclotomic field Q（ξPl） with odd degree, F be the group of cyclotomic unitsof K, and F+ be the group of totally positive cyclotomic units of K. By calculating dim F2 F+/F2, we getan elementary criterion of parity of class number of field K. From this, we proved that in the （cyclic）subfields of cyclotomic field Q（ξPl） （p1000） with odd degree n（3≤n≤19） there exist just 17 fields witheven class number.