The Riemann Hypothesis is false

Read full text
Authors: Tatenda Kubalalika
Cited by: 0

Abstract

Let $\Theta$ denote the supremum of the real parts of the zeros of the Riemann zeta function $\zeta(s)$. By carefully exploiting the Landau-Gonek explicit formula, the Dirichlet polynomial approximation of $\zeta(s)$ and other classical results in analytic number theory, we rigorously demonstrate that $\Theta=1$. This entails the existence of infinitely many Riemann zeros off the critical line (thus disproving the Riemann Hypothesis (RH)). The paper is concluded by a brief discussion of why our argument does not work for both Weil and Beurling zeta functions, whose analogues of the RH are known to be true.

Fields of Study & Subjects

Analytic Number Theory Research Advanced Mathematical Identities Limits and Structures in Graph Theory

Publication details

Publication date
13 February 2026
Language
EN
Document type
Preprint