An Elementary Problem Equivalent to the Riemann Hypothesis

TL;DR

This paper presents an elementary reformulation of the Riemann hypothesis, demonstrating its equivalence to a sequence of simple inequalities involving harmonic numbers, building on Robin's criterion.

Contribution

It introduces a new elementary criterion for the Riemann hypothesis based on inequalities with harmonic numbers, simplifying the problem.

Findings

Riemann hypothesis is equivalent to specific inequalities involving harmonic numbers.

The criterion is a modification of Robin’s existing criterion.

Provides a potentially more accessible approach to the hypothesis.

Abstract

This paper shows the equivalence of the Riemann hypothesis to an sequence of elementary inequalities involving the harmonic numbers H_n, the sum of the reciprocals of the integers from 1 to n. It is a modification of a criterion due to Guy Robin.