On the prime zeta function and the Riemann hypothesis
General Mathematics
2021-02-26 v7
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.
Keywords
Cite
@article{arxiv.1910.02954,
title = {On the prime zeta function and the Riemann hypothesis},
author = {Tatenda Kubalalika},
journal= {arXiv preprint arXiv:1910.02954},
year = {2021}
}
Comments
The propoed proof is flawed. In particular, the analyticity of the function F(s) in s>1/2 was not properly established, and is actually equivalent to the Riemann Hypothesis