Additive arithmetic functions meet the inclusion-exclusion principle, II

TL;DR

This paper unifies results on additive arithmetic functions using series involving the Riemann zeta function and prime sums, extending previous work in the field.

Contribution

It introduces a broad class of additive functions and provides a unified framework for their analysis, building on earlier results.

Findings

Unified results for additive functions

Use of Riemann zeta function series

Analysis of prime sums

Abstract

We unify in a large class of additive functions the results obtained in the first part of this work. The proof rests on series involving the Riemann zeta function and certain sums of primes which may have their own interest.