A note on the modified q-Dedekind sums

TL;DR

This paper introduces a p-adic q-analogue of higher order modified Dedekind sums linked to q-Genocchi polynomials, utilizing fermionic p-adic invariant q-integrals to explore their properties.

Contribution

It develops a new p-adic q-analogue of Dedekind sums related to q-Genocchi polynomials using fermionic p-adic integrals, extending existing number theory concepts.

Findings

Defined a p-adic continuous function for odd primes.

Established properties of the modified q-Dedekind sums.

Connected sums to q-Genocchi polynomials.

Abstract

In the present paper, the fundamental aim is to consider a p-adic continuous function for an odd prime to inside a p-adic q-analogue of the higher order modified Dedekind-type sums related to q-Genocchi polynomials with weight alpha by using fermionic p-adic invariant q-integral on Zp.