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**New Theories / Re: What makes Riemann's Hypothesis Hard to Prove?**

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**Today**at 18:12:05 »

In transition zone between 2 π i and (2+β) πi, S function crosses zero more than once. It is corresponding to critical strip. Below 2 π i, S function in critical strip has positive slope. It's corresponding to real line >1.

Exploration of backslash function (aka S function) around its inflection point can be exciting in its own right, but does not have much effect on the determination of Riemann hypothesis, which for now has narrowed down to critical strip with extremely high imaginary part.The behavior of S function around its inflection point reminds me of Riemann sphere.Quotehttps://en.wikipedia.org/wiki/Riemann_sphere

In mathematics, the Riemann sphere, named after Bernhard Riemann,[1] is a model of the extended complex plane (also called the closed complex plane): the complex plane plus one point at infinity. This extended plane represents the extended complex numbers, that is, the complex numbers plus a value ∞ for infinity. With the Riemann model, the point ∞ is near to very large numbers, just as the point 0 is near to very small numbers.

Here's an online simulator.

https://www.geogebra.org/m/gD7Rygd2