p-adic interpolation function related to multiple generalized Genocchi numbers

TL;DR

This paper introduces a p-adic interpolation function for multiple generalized Genocchi numbers and polynomials, defining a new p-adic L-function and analyzing its properties at specific points.

Contribution

It presents the first analytic p-adic interpolation function for multiple generalized Genocchi numbers and defines a related p-adic L-function with derivative evaluations.

Findings

Defined the multiple Genocchi p-adic L-function

Established the interpolation at negative integers

Calculated the partial derivative at s=0

Abstract

In the present paper, we deal with multiple generalized Genocchi numbers and polynomials. Also, we introduce analytic interpolating function for the multiple generalized Genocchi numbers attached to \c{hi} at negative integers in complex plane and we define the multiple Genocchi p-adic L-function. Finally, we derive the value of the partial derivative of our multiple p-adic l-function at s=0.