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Quote from: hamdani yusuf on 11/05/2024 01:19:45After watching a video about elliptic curve, I suspected that trivial zeros of Zeta function must somehow be related to non-trivial zeros. This video shows how they are related.The video shows that non-trivial zeros of Riemann's Zeta function must somehow be correlated to its trivial zeros. I think it's worth exploring if other points on the critical line are also correlated to points on the real line through some sort of mapping or projection.
After watching a video about elliptic curve, I suspected that trivial zeros of Zeta function must somehow be related to non-trivial zeros. This video shows how they are related.
Quote from: hamdani yusuf on 19/05/2024 09:57:19Exploration 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_sphereIn 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
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.
https://en.wikipedia.org/wiki/Riemann_sphereIn 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.
Plotted symmetrically, it looks like the letter V. So, I'll just call it V function.
Quote from: hamdani yusuf on 17/05/2024 05:14:38We get a nice full wave when the imaginary part is exactly 2*pihttps://www.wolframalpha.com/input?i=plot+re%28log%28zeta%28x%2B+2+pi+i%29+%2F%28Zeta%281-x%2B+2+pi+i%29%29%29%29from+0+to+1
We get a nice full wave when the imaginary part is exactly 2*pi