Abstract
The Riemann Hypothesis, formulated by Bernhard Riemann in his seminal 1859 manuscript, remains one of the most critical and longstanding open problems in analytic number theory. A definitive proof or counterexample would have profound ramifications, extending beyond number theory into areas such as quantum physics, cryptography, and information theory. This work aims to establish a proof of the Riemann Hypothesis by employing a novel, as yet unpublished, theorem in complex analysis. This theorem leverages the holomorphic properties of the Riemann zeta function to rigorously relate the distribution of zeros and poles within a specified region of its domain to another region where the function remains analytic, non-vanishing, and devoid of singularities. By proving and applying this new result, we present a complete demonstration of the Riemann Hypothesis.
Access the article for more information:
Gomes, E. R. P. (2025). Holomorphism of the Zeta Function and the Proof of the Riemann Hypothesis (Versão V2). Zenodo. https://doi.org/10.5281/zenodo.15338333
