对Kummer-Hilbert互逆定律的又一种证明方法

Another Methods of Proof of Kummer-Hilbert Reciprocity Law

Kummer Hilbert互逆定律的最初证明是从Hilbert符号及Kummer素循环体的理论出发而推导出来的.在此我们在Kummer建立起来的素循环体理论的基础上,运用p进循环体中k中的主单位及素元的性质以及由k中主单位及素元定义的对数微商l(i)π(υ)的范数理论,从数论的角度给出该定律的另一种证明方法.

The primitive proof of the Kummer-Hilbert reciprocity law was deduced from Hilbert symbol and the theory of a Kummer's prime cyclotomic field.On the basis of theory of a Kummer's prime cyclotomic field we make use of the %p%-adic the propositions of principal unit and prime element, the theory of the norm that defined logarithmic derivatives %l+{(i)}-π(υ)% by principal unit and prime element in %k%,the another methods of proof of the Kummer-Hilbert reciprocity law is given from the view point of the number theory.