The Riemann Hypothesis is false
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