Dear esteemed mathematicians,
I am excited to share with you our recent research exploring novel chaotic dynamics derived from the Riemann and von Mangoldt function formula, specifically focusing on the distribution of nontrivial zeros of the Riemann zeta function. Our findings are detailed in the paper accessible through the following link:
https://arxiv.org/abs/2404.00583
Here is the abstract of my paper:
In our study, we investigate the behavior of these dynamics by computing Lyapunov exponents, revealing chaotic behavior within a certain threshold of gaps between zeros, up to 2.4. Additionally, we introduce a new chaotic operator for the Riemann zeta function within the critical strip, incorporating the correction term from the Riemann-von Mangoldt formula. We establish the chaotic nature and Hermiticity of this operator, alongside discussing its diagonalization properties.
Furthermore, our research uncovers intriguing parallels between our derived chaotic operator and the quantum hydrogen model, as indicated by the similarity of its eigenvalues to the energy levels of hydrogen. Various numerical analyses, including Lyapunov exponents, bifurcation analysis, and entropy computation, highlight the unpredictable nature of the system.
Moreover, we establish a connection between our chaotic operator and the prime number theorem concerning the density of primes. Importantly, our investigation suggests strong support for the validity of the Riemann hypothesis through this chaotic operator, aligning with propositions made by Hilbert and Polya.
These findings illuminate the intricate interplay between chaotic dynamics, number theory, and quantum mechanics, providing fresh insights into the behavior of the Riemann zeta function and its zeros. We further demonstrate the Hermiticity and diagonalization properties of our operator using the spectral theorem, offering deeper understanding into its mathematical characteristics and unboundedness.
We invite your valuable insights and expertise on our research findings and hypotheses. Your comments and critiques would be greatly appreciated in refining and validating our work.
Thank you for considering our research
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