We derive the existence of p-adic Hurwitz–Lerch L-function by means of a method provided by Washington. This function is a generalization of the one-variable p-adic L-function of Kubota and Leopoldt, and two-variable p-adic L-function of Fox. We also deduce divisibility properties of generalized Apostol–Bernoulli polynomials, in particular establish Kummer-type congruences for them.

中文翻译：

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p-adic Hurwitz-Lerch L 函数的构造

我们通过华盛顿提供的方法推导出 p-adic Hurwitz-Lerch L 函数的存在。该函数是 Kubota 和 Leopoldt 的单变量 p-adic L 函数和 Fox 的双变量 p-adic L 函数的推广。我们还推导出广义 Apostol-Bernoulli 多项式的可分性，特别是为它们建立 Kummer 型同余。