On the prime zeta function and the Riemann hypothesis

Tatenda Kubalalika

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arXiv · 1910.02954

On the prime zeta function and the Riemann hypothesis

Tatenda Kubalalika

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Abstract

By considering the prime zeta function, the author intended to demonstrate in that the Riemann zeta function zeta(s) does not vanish for Re(s)>1/2, which would have proven the Riemann hypothesis. However, he later realised that the proof of "Theorem 3" is fundamentally flawed. The main tools of our argument are: bounds and oscillation theorems for the prime counting function, classical properties of Dirichlet series and the identity theorem for real-analytic functions.

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Tatenda Kubalalika. 2021-02-25. On the prime zeta function and the Riemann hypothesis. https://arxiv.org/abs/1910.02954

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