Riemann Hypothesis for dynamical systems

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SUMMARY

The discussion centers on the Riemann Hypothesis (RH) and its relation to differential equations in dynamical systems. Participants reference an article from the Journal de Physique that explores the connection between the zeta function and the S-plane, emphasizing the significance of the non-trivial zeros located on the critical line of 1/2. The conversation highlights the geometric interpretation of these zeros as right angles to the real line, suggesting an intuitive understanding of RH. However, no definitive proof of the Riemann Hypothesis has been established by the authors of the referenced article.

PREREQUISITES
  • Understanding of the Riemann Zeta Function
  • Familiarity with complex analysis and the S-plane
  • Knowledge of differential equations in dynamical systems
  • Basic concepts of non-trivial zeros in number theory
NEXT STEPS
  • Research the implications of the Riemann Hypothesis on number theory
  • Study the properties of the Riemann Zeta Function and its zeros
  • Explore differential equations related to dynamical systems
  • Investigate existing proofs and conjectures surrounding the Riemann Hypothesis
USEFUL FOR

Mathematicians, theoretical physicists, and students interested in number theory and dynamical systems, particularly those exploring the implications of the Riemann Hypothesis.

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Thanks for the link. should be an interesting link.

Yet for the facts that the input to the function is based upon a right angle intersection of the real to imaginary being the input to the zeta function, output to the S plane directly related to this.
This of course being the output of zeros being on the r,i plane from the s plan, and the non trivial zeroes being such that they are every negative even integer.
It should be easy for people to see that the non trivial zeros are as a right angle to the real line. For that mater it should be easy for people to see due to input method that a variation of the trivial zeros (which does not exist) would have to result for a non trivial zero to be of the real part line of 1/2.
It is a built in given of the input.

Writing a proof to show this... LOL good luck, yet it does show the intuitive reasoning of RH.
 

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