p-adic Dedekind and Hardy-Berndt type sum related to Volkenborn Integral on Z_p

TL;DR

This paper develops p-adic Dedekind and Hardy-Berndt sums, constructs related generating functions for twisted Bernoulli polynomials, and explores elliptic analogues of Apostol-Dedekind sums within the p-adic setting.

Contribution

It introduces new p-adic Dedekind and Hardy-Berndt sums and their generating functions, extending classical sums into the p-adic and elliptic frameworks.

Findings

Construction of p-adic Dedekind sums and Hardy-Berndt sums

Development of generating functions for twisted Bernoulli polynomials

Discussion on elliptic analogues of Apostol-Dedekind sums

Abstract

The purpose of this paper is to construct p-adic Dedekind sums and Hardy-Berndt type sums. We also construct generating function of the twisted Bernoulli polynomials and functions. Furthermore, we give some discussions on elliptic analogue of the Apostol-Dedekind sums.