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Non trivial zeros of the Riemann zeta function

18 February 2025, Version 16
Working Paper
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.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 $\Re(s)\in (0,\frac{1}{2})$.

Keywords

Zeta function
Non trivial zeros

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Version History

Feb 18, 2025 Version 16

Version Notes

To simplify the reading, in this version, the Riemann Zeta function has been considered instead of the generalized function.

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License

All Rights Reserved

DOI

10.33774/coe-2023-sb63n-v16
D O I: 10.33774/coe-2023-sb63n-v16 [opens in a new tab]

Author’s competing interest statement

The author(s) have declared they have no conflict of interest with regard to this content

Ethics

The author(s) declare that they have sought and gained approval from the relevant ethics committee/IRB for this research and its publication.

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