Smooth arithmetical sums over k-free integers

TL;DR

This paper investigates the asymptotic behavior of smooth arithmetical sums over k-free integers using partial zeta functions, providing new insights into their distribution and properties.

Contribution

It introduces a novel analytical approach employing partial zeta functions to study smooth sums over k-free integers, advancing understanding in number theory.

Findings

Derived asymptotic formulas for sums over k-free integers

Established connections between partial zeta functions and smooth sums

Enhanced methods for analyzing distribution of k-free integers

Abstract

We use partial zeta functions to analyse the asymptotic behaviour of certain smooth arithmetical sums over smooth k-free integers.