Dear Researchers,
I am reaching out to seek insights and opinions on the potential connections between chaotic dynamics, arithmetic functions, and open conjectures in analytic number theory. My interest lies in exploring the derivation of chaotic operators from mathematical constructs such as L-Dirichlet functions and conjectures like those presented by Yitang Zhang in 2022 on Landau-Siegel zeros, as well as the Montgomery conjecture on the distribution of zeros.
Specifically, I am intrigued by the possibility of deriving chaotic dynamics from these mathematical frameworks and understanding their implications for questions related to the Riemann Hypothesis.
I also want to inform you that I have recently derived a chaotic operator from Yitang Zhang's latest theorem on Landau-Siegel zeros. The work has been accepted for publication in the European Physical Journal.
My ultimate goal is to further investigate the derivation of chaotic operators from these mathematical foundations and to understand the conditions under which ζ(0.5+iH)=0. welcome any insights, suggestions, or collaboration opportunities that may arise from your expertise in these areas.
Thank you for your time and consideration. I look forward to engaging in fruitful discussions with the research community.
There's considerable activity on all these topics, so it would be a good idea to learn to focus on the technical content rather than the sociology.
Anyone that expects to prove the Riemann hypothesis this way is bound to be disappointed-because there are a lot of intermediate results to prove, first, in order to establish how it fits in. So it would be a good idea to start by not making a fool of oneself with statements full of buzzwords, that just don't make sense, but focus on learning something about the subject of ``arithmetical chaos'', assuming that's what one wants to do.
Laymen focus on conjectures, out of context, professionals focus on learning what they mean. The reason conjectures aren't theorems, yet, is that their content isn't understood. They become theorems when the correct way of formulating them becomes understood. Whether the Riemann hypothesis has anything to do with chaotic dynamics at all isn't that obvious. It is possible to describe many aspects of chaotic dynamics without having to mention once the Riemann hypothesis.
This article: https://people.maths.bris.ac.uk/~majm/bib/arithmetic.pdf
might be useful as an overview of arithmetic chaos.
As might this summary http://www.scholarpedia.org/article/Arithmetical_quantum_chaos of a review article. Article Arithmetical chaos
and this: Article Quantum and Arithmetical Chaos
Along with papers by Rudnick, http://www.math.tau.ac.il/arithmeticQC/about/ and Sarnak, https://web.math.princeton.edu/sarnak/Arithmetic%20Quantum%20Chaos.pdf
I would like to note the following, since what is written in the previous post about conjectures and theorems may create confusion. All conjectures are meaningful and well-stated mathematical statements. What distinguishes a conjecture from a theorem is the existence of a valid proof. Conjectures are statements that are believed to be true, but they have not been proven yet, while theorems are statements that have been proven. For instance, the famous Fermat’s last theorem had actually been a conjecture before it was proven, in 1995, and since then, it has been a theorem. It is also worth mentioning that many conjectures have been proven to be false by providing counterexamples. Clearly, the Riemann hypothesis is (still) a conjecture.
For the readers : https://mathworld.wolfram.com/Theorem.html,
https://mathworld.wolfram.com/Conjecture.html
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