Partial Liouville sums over divisors

TL;DR

This paper demonstrates that the signs of partial sums of the Liouville function over divisors are evenly distributed, using sieve methods and elementary techniques.

Contribution

It introduces a new elementary approach to analyze the sign distribution of partial Liouville sums over divisors.

Findings

Signs of partial Liouville sums are equally distributed

Elementary methods can effectively analyze divisor sums

Provides insights into the sign behavior of Liouville function sums

Abstract

Using sieves and elementary manipulations, we show that the signs of partial sums of the Liouville function over divisors are in a strong sense equally distributed.