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This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.
Abstract
In this paper, we consider the representation of the Riemann zeta function $\zeta$ defined by Abel's summation formula. We show that $|\zeta(s)|\neq 0$ for any point $s\in \mathbb{C}$ such that $\Re(s)\in (0,\frac{1}{2})$.