论文标题
poly-dedekind总和上的身份
Identities on poly-Dedekind sums
论文作者
论文摘要
Dedekind总和发生在模块化组的替换下的Dedekind ETA功能的对数的转换行为中。 1892年，Dedekind展示了Dedekind总和的互惠关系。 Apostol通用的Dedekind总和通过替换任何Bernoulli函数出现的第一个Bernoulli函数，并得出了广义Dedekind Sums的相互关系。在本文中，我们考虑了通过Dedekind总和从Dedekind总和中获得的多型二级总和，通过将第一个bernoulli函数替换为任意索引的任何类型的poly-bernoulli函数，并证明了poly-dedekind总和的互惠关系。
Dedekind sums occur in the transformation behaviour of the logarithm of the Dedekind eta-function under substitutions from the modular group. In 1892, Dedekind showed a reciprocity relation for the Dedekind sums. Apostol generalized Dedekind sums by replacing the first Bernoulli function appearing in them by any Bernoulli functions and derived a reciprocity relation for the generalized Dedekind sums. In this paper, we consider poly-Dedekind sums which are obtained from the Dedekind sums by replacing the first Bernoulli function by any type 2 poly-Bernoulli functions of arbitrary indices and prove a reciprocity relation for the poly-Dedekind sums.
