Riemann Hypothesis Disproved - New Complex Zeros of Zeta Function Found off the Critical Line in the Critical Strip

Abstract

In the mid of the 19th Century the world-renowned Mathematician Bernhard Riemann stated in his Riemann hypothesis that all complex zeros would lie on the ½ line which is called the "critical line". Although trillions of complex zeros have been found using numerical computational methods, till this day, no other complex zero off the critical line have been found. Using the Zeta function derived by Leonard Euler from the Dirichlet eta function, it is found that there exist at least two other non-trivial zeros which do not lie on the critical line but are included in the critical strip between 0 and 1. These complex zeros have a real part of just slightly smaller than 1. The newly found complex zeros off the critical line provide counter examples to the Riemann hypothesis.

Locations

• SSRN Electronic Journal - View
• Zenodo (CERN European Organization for Nuclear Research) - View - PDF
• OSF Preprints (OSF Preprints) - View - PDF