Proving the Riemann Hypothesis with Probability One

Naoh Y and Chukwa K

Published on: 2024-10-25

Abstract

The Riemann Hypothesis (R.H) claims that the non-trivial zeros of the zeta function ζ(s) have a real value equal to 1/2. This hypothesis has been one of the main unsolved issues for number-theorists worldwide. This paper will attempt to prove the hypothesis in a weaker form. In Section 2 we discuss the preliminaries needed to prove this hypothesis. In Section 3 we simplify the R.H by connecting the Mertens function with a probabilistic interpretation. In Section 4, a proof that the R.H is true with a probability of 1 is given.

Keywords

Riemann Hypothesis, Number Theory, Arithmetic Functions, Probability

Introduction

 

The Riemann Hypothesis (R.H) claims that the non-trivial zeros of the zeta function ζ(s) have a real value equal to 1/2. This hypothesis has been one of the main unsolved issues for number-theorists worldwide. This paper will attempt to prove the hypothesis in a weaker form. In Section 2 we discuss the preliminaries needed to prove this hypothesis. In Section 3 we simplify the R.H by connecting the Mertens function with a probabilistic interpretation. In Section 4, a proof that the R.H is true with a probability of 1 is given.