On an arithmetical approach to the Riemann hypothesis

TL;DR

This paper proposes a new sufficient condition involving the Liouville function's partial sums that, if satisfied, implies the Riemann hypothesis, and presents a related intriguing formula.

Contribution

It introduces a novel sufficient condition for the Riemann hypothesis based on the magnitude of Liouville function sums and explores a related mathematical formula.

Findings

Proves a sufficient condition for the Riemann hypothesis.

Derives a formula related to the sufficient condition.

Provides insights into the behavior of the Liouville function.

Abstract

In the paper, we first prove a sufficient condition for the Riemann hypothesis which involves the order of magnitude of the partial sum of the Liouville function. Then we show a formula which is curiously related to the proved sufficient condition.