Character Sums and the Riemann Hypothesis

TL;DR

This paper links a simple inequality involving character sums to the Riemann Hypothesis, proposing a new approach via sums of Legendre symbols to potentially prove this famous conjecture.

Contribution

It establishes a novel connection between a basic inequality and the Riemann Hypothesis, suggesting a new method for approaching the problem.

Findings

Inequality implies the Riemann Hypothesis

Approach involves sums of Legendre symbols

Provides a new perspective on the conjecture

Abstract

We prove that an innocent looking inequality implies the Riemann Hypothesis and show a way to approach this inequality through sums of Legendre symbols.