A note on the q-Dedekind-type Daehee-Changhee sums with weight alpha arising from modified q-Genocchi polynomials with weight alpha

TL;DR

This paper explores a p-adic q-analogue of higher order Dedekind-type sums with weight, connecting them to modified q-Genocchi polynomials through p-adic invariant q-integrals, expanding the mathematical framework of these sums.

Contribution

It introduces a new p-adic q-analogue of Dedekind-type sums with weight linked to modified q-Genocchi polynomials using p-adic invariant q-integrals.

Findings

Defined a p-adic continuous function for odd primes

Established a connection between Dedekind-type sums and q-Genocchi polynomials

Provided properties of the new sums in the p-adic setting

Abstract

In the present paper, our objective is to treat a p-adic continuous function for an odd prime to inside a p-adic q-analogue of the higher order Dedekind-type sums with weight in connection with modified q-Genocchi polynomials with weight alpha by using p-adic invariant q-integral on Zp.