论文标题
涉及聚欧拉函数的poly-dedekind型直流总和
poly-Dedekind type DC sums involving poly-Euler functions
论文作者
论文摘要
经典的Dedekind总和出现在模块化组的替换下的Dedekind Eta功能对数的转换行为中。 Dedekind总和及其概括是根据Bernoulli函数及其概括来定义的，并被证明满足了一些互惠关系。相反，Dedekind类型DC（Daehee和Changhee）和它们的概括是根据Euler函数及其概括来定义的。本文的目的是介绍多型型型DC总和，这些总和是通过Dedekind Type DC总和获得的，通过通过任意索引的多欧拉函数替换Euler函数，并表明这些和表明这些总和满足其他事项，除其他事项外，还满足了相互关系。
The classical Dedekind sums appear in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group. The Dedekind sums and their generalizations are defined in terms of Bernoulli functions and their generalizations, and are shown to satisfy some reciprocity relations. In contrast, Dedekind type DC (Daehee and Changhee) sums and their generalizations are defined in terms of Euler functions and their generalizations. The purpose of this paper is to introduce the poly-Dedekind type DC sums, which are obtained from the Dedekind type DC sums by replacing the Euler function by poly-Euler functions of arbitrary indices, and to show that those sums satisfy, among other things, a reciprocity relation.
