【摘要】 Ｄｅｄｅｋｉｎｄ和的Ｋｎｏｐｐ等式是与Ｈｅｃｋｅ算子有关的一个算术性质，本文不借助ｅｔａ－函数的概念，给予Ｋｎｏｐｐ等式的一个简短的初等证明，同时把Ｋｎｏｐｐ等式拓广到广义Ｄｅｄｅｋｉｎｄ和中。更多还原

【Abstract】 Knopp’s identity for the classical Dedeklnd sums is an interesting arithmetical propo-sition related to Hecke operators: In this note,we give an elementary proof of the identity, whichdon’t depend upon Dedekind eta-function. We also ewtend it to generalized Dedekind sums.更多还原