On a General Class of A-functions

TL;DR

This paper introduces a broad new class of A-functions, generalizing existing classes, and explores their algebraic properties and implications for rational arithmetical functions.

Contribution

It defines a new, comprehensive class of A-functions that unifies and extends previous classes, providing new algebraic insights and results.

Findings

New algebraic properties of A-functions derived

Generalization encompasses regular, structured, and perfect A-functions

Results applicable to rational arithmetical functions

Abstract

Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions. Algebraic results are discussed and analysis is performed to deduce new results concerning rational arithmetical functions.