Two generalizations of the Busche-Ramanujan identities

TL;DR

This paper introduces two new generalizations of the Busche-Ramanujan identities, expanding their applicability through multiple Dirichlet convolutions and symmetric polynomial properties.

Contribution

It presents novel generalizations of classical identities using advanced techniques like multiple Dirichlet series and symmetric polynomials.

Findings

Derived two new identities involving multiple Dirichlet convolutions

Utilized formal multiple Dirichlet series in proofs

Connected identities with properties of symmetric polynomials

Abstract

We derive two new generalizations of the Busche-Ramanujan identities involving the multiple Dirichlet convolution of arithmetic functions of several variables. The proofs use formal multiple Dirichlet series and properties of symmetric polynomials of several variables.