Note on q-Dedekind type sums related to q-Euler polynomials

TL;DR

This paper constructs a p-adic continuous function that generalizes higher order Dedekind sums related to q-Euler polynomials using q-analogs, advancing the understanding of p-adic and q-analogue number theory.

Contribution

It introduces a new p-adic q-analogue of Dedekind sums linked to q-Euler polynomials, expanding the theoretical framework in p-adic analysis.

Findings

Defined a p-adic continuous function for odd primes

Established a q-analogue of higher order Dedekind sums

Connected Dedekind sums with q-Euler polynomials

Abstract

it is the purpose of this paper to construct a p-adic continuous function for an odd prime to contain a p-adic q-analogue of higher order Dedekind type sums related to q-Euler polynomials and numbers.