On some identities in multiplicative number theory

TL;DR

This paper proves new identities involving the Möbius function using elementary methods, extending well-known formulas to multidimensional cases through convolution arguments.

Contribution

It introduces generalized identities for the Möbius function in multiple dimensions, expanding the scope of classical number theory formulas.

Findings

Derived several new identities involving the Möbius function

Extended classical formulas to multidimensional settings

Used elementary methods for proofs

Abstract

Using elementary means, we prove several identities involving the M\"obius function, generalizing in the multidimensional case well-known formulas coming from convolution arguments.