论文标题
LERCH ZETA函数在Holomorphy的最大结构域上的明确表达
An explicit expression of the Lerch zeta function on maximal domains of holomorphy
论文作者
论文摘要
我们在lerch zeta函数$φ（z，\，s，\，w）$上给出了两个结果。 The first is to give an explicit expression providing both the analytic continuation of $Φ$ in $n$-variables $(n \in \{1,\,2,\,3\})$ to maximal domains of holomorphy in $\mathbb{C}^n$ with computable evaluation and an extended formula for the special values of $Φ$ at non-positive integers in the variable $ S $。第二个是证明LERCH的功能方程与使用第一个结果的功能方程基本相同。
We give two results on the Lerch zeta function $Φ(z,\,s,\,w)$. The first is to give an explicit expression providing both the analytic continuation of $Φ$ in $n$-variables $(n \in \{1,\,2,\,3\})$ to maximal domains of holomorphy in $\mathbb{C}^n$ with computable evaluation and an extended formula for the special values of $Φ$ at non-positive integers in the variable $s$. The second is to show that Lerch's functional equation is essentially the same as Apostol's functional equation using the first result.
