![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){kind=logo}
Abstract
In this paper, the generalized Riemann Zeta function is defined on the right half-plane. In particular, this allows us to prove that for every $\tau\in \mathbb{R}$ there exists at most one point $r\in (0,1)$ such that $|\zeta(r+i\tau) |=0$.