Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The Riemann Hypothesis is false

Tatenda Kubalalika

Abstract

Let $Θ$ denote the supremum of the real parts of the zeros of the Riemann zeta function. We demonstrate that $Θ=1$, which entails the existence of infinitely many Riemann zeros off the critical line (thus disproving the Riemann Hypothesis (RH), which asserts that $Θ= \frac{1}{2}$). The paper is concluded by a brief discussion of why our argument doesn't work for both Weil and Beurling zeta functions whose analogues of the RH are known to be true.

The Riemann Hypothesis is false

Abstract

Let denote the supremum of the real parts of the zeros of the Riemann zeta function. We demonstrate that , which entails the existence of infinitely many Riemann zeros off the critical line (thus disproving the Riemann Hypothesis (RH), which asserts that ). The paper is concluded by a brief discussion of why our argument doesn't work for both Weil and Beurling zeta functions whose analogues of the RH are known to be true.

Paper Structure

This paper contains 32 equations.

Theorems & Definitions (2)

  • proof
  • proof