论文标题
在与广义除数功能有关的一些$ q $ series身份及其含义
On some $q$-series identities related to a generalized divisor function and their implications
论文作者
论文摘要
在本文中，Kluyver和Uchimura检查的$ Q $ Series被广泛化。这使我们能够在1993年由Simon，Crippa和Collenberg研究的随机无环挖掘中找到身份的概括。作为我们主要定理的推论之一，我们获得了Dilcher和Andrews，Crippa和Simon的结果。该主要定理涉及对除数函数$σ_s（n）$的令人惊讶的新概括，我们用$σ_{s，z}（n）$表示。还研究了$σ_{s，z}（n）$的分析属性。作为我们定理之一的特殊情况，我们从最近的Bringmann和Jennings-Shaffer的论文中获得了结果。
In this article, a $q$-series examined by Kluyver and Uchimura is generalized. This allows us to find generalization of the identities in the random acyclic digraph studied by Simon, Crippa, and Collenberg in 1993. As one of the corollaries of our main theorem, we get results of Dilcher and Andrews, Crippa, and Simon. This main theorem involves a surprising new generalization of the divisor function $σ_s(n)$, which we denote by $σ_{s,z}(n)$. Analytic properties of $σ_{s,z}(n)$ are also studied. As a special case of one of our theorem we obtain result from a recent paper of Bringmann and Jennings-Shaffer.
