Non trivial zeros of the generalized  Zeta function

Walid OUKIL

doi:10.33774/coe-2023-sb63n-v9

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Non trivial zeros of the generalized Zeta function

08 August 2024, Version 9

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Working Paper

Walid OUKIL

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This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.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

We define the generalized Riemann Zeta function on the right half plane. We prove, in particular, that for every $\tau\in \mathbb{R}$ there exists at most one point $r\in (0,1)$ such that $|\zeta(r+i\tau) |=0$.

Keywords

Zeta function

Non trivial zeros

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Version History

Version Notes

This version is same as the last version. We use another method to prove Theorem (2) from the previous version. This method uses induction instead of iterating the operator \Phi_*.

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DOI

10.33774/coe-2023-sb63n-v9

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.