Class numbers of cyclic 2-extensions and Gross conjecture over Q  

作　　者：Ouyang Yi Xue Hang 

机构地区：[1]Univ Sci & Technol China, Dept Math, Hefei 230026, Peoples R China

出　　处：《Science China Mathematics》2010年第9期2447-2462,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.10871183);Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.200803580047)

摘　　要：The Gross conjecture over Q was first claimed by Aoki in 1991.However,the original proof contains too many mistakes and false claims to be considered as a serious proof.This paper is an attempt to find a sound proof of the Gross conjecture under the outline of Aoki.We reduce the conjecture to an elementary conjecture concerning the class numbers of cyclic 2-extensions of Q.The Gross conjecture over Q was first claimed by Aoki in 1991.However,the original proof contains too many mistakes and false claims to be considered as a serious proof.This paper is an attempt to find a sound proof of the Gross conjecture under the outline of Aoki.We reduce the conjecture to an elementary conjecture concerning the class numbers of cyclic 2-extensions of Q.

关 键 词：GROSS CONJECTURE class NUMBER CYCLIC 2-extension 

分 类 号：N[自然科学总论]