Abstract
This paper introduces a novel analytic framework to study the distribution of non-trivial zeros of the Riemann zeta function. By constructing a specialized atomic system in the Hardy space H2(C+), we prove that ζ(ρ) does not vanish in any compact region away from the critical line. This result provides new insights into the behavior of zeta zeros, independent of the Riemann Hypothesis.



![Author ORCID: We display the ORCID iD icon alongside authors names on our website to acknowledge that the ORCiD has been authenticated when entered by the user. To view the users ORCiD record click the icon. [opens in a new tab]](https://www.cambridge.org/engage/assets/public/coe/logo/orcid.png)