Proposed (dis)proofs of the Riemann Hypothesis
"Without doubt it would be desirable to have a rigorous proof of this proposition; however I have left this research aside for the time being after some quick unsuccessful attempts, because it appears to be unnecessary for the immediate goal of my study..."
If you are a university mathematics lecturer who teaches analytic number theory, you might want to consider setting your students the task of deconstructing the more serious of these. They may otherwise never be given any serious attention, which would be a shame. As someone once joked, "It's easier to prove the RH than to get someone to read your proof!" D. Biswas, "Analytical expression of complex Riemann xi function $\xi(s)$ and proof of Riemann Hypothesis"
[abstract:] "In this paper explicit analytical expression for Riemann xi function $\xi(s)$ is worked out for complex values of $s$. From this expression Riemann Hypothesis is proved. Analytic Expression for non-trivial zeros of Riemann zeta function $\zeta(s)$ is also found. A second proof of Riemann Hypothesis is also given" J. Feliksiak, "The elementary proof of the Riemann's Hypothesis"
[abstract:] "This research paper aims to explicate the complex issue of the Riemann's Hypothesis and ultimately presents its elementary proof. The method implements one of the binomial coefficients, to demonstrate the maximal prime gaps bound. Maximal prime gaps bound constitutes a comprehensive improvement over the Bertrand's result, and becomes one of the key elements of the theory. Subsequently, implementing the theory of the primorial function and its error bounds, an improved version of the Gauss' offset logarithmic integral is developed. This integral serves as a Supremum bound of the prime counting function $\pi(n)$. Due to its very high precision, it permits to verify the relationship between the prime counting function $\pi(n)$ and the offset logarithmic integral of Carl Gauss. The collective mathematical theory, via the Niels F. Helge von Koch equation, enables to prove the Riemann's Hypothesis conclusively."
