On $p$-adic Hurwitz-type Euler zeta functions

Min-Soo Kim; Su Hu

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arXiv · 1010.2269

On $p$-adic Hurwitz-type Euler zeta functions

Min-Soo Kim·Su Hu

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Abstract

The definition for the $p$-adic Hurwitz-type Euler zeta functions has been given by using the fermionic $p$-adic integral on $\mathbb Z_p$. By computing the values of this kind of $p$-adic zeta function at negative integers, we show that it interpolates the Euler polynomials $p$-adically. Many properties are provided for the $p$-adic Hurwitz-type Euler zeta functions, including the convergent Laurent series expansion, the distribution formula, the functional equation, the reflection formula, the derivative formula, the $p$-adic Raabe formula and so on. The definition for the $p$-adic Euler $L$-functions has also been given by using the $p$-adic Hurwitz-type Euler zeta functions.

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Min-Soo Kim, Su Hu. 2010-10-12. On $p$-adic Hurwitz-type Euler zeta functions. https://arxiv.org/abs/1010.2269

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