Hi everyone, I’ve recently made a surprising yet fascinating discovery that I’d like to share with you. While exploring visualizations of the Riemann zeta function and Dirichlet L-functions, I observed a striking self-similar pattern emerging within iterations of the Mandelbrot set. I’ve attached some images that highlight these intriguing parallels.

Through this exploration, we identified the fractal structure of the analytic continuation of the Riemann zeta function. Notably, both the analytic continuation and the fractal derived from the Mandelbrot set are defined on the same complex plane, allowing for a direct geometric and spectral comparison.

It appears that the non-trivial zeros correspond to a quantum mechanical system with both spectral and dynamic properties—providing strong support for the Hilbert–Pólya conjecture.

It has long been suggested that if such a quantum system can be explicitly identified—one whose eigenvalues align with the imaginary parts of the non-trivial zeros—then the Hilbert–Pólya conjecture, and consequently the Riemann Hypothesis, would be confirmed. Our findings offer compelling evidence in this direction, combining insights from fractal geometry, spectral theory, and quantum physics to shed light on one of mathematics’ greatest unsolved problems. Additionally, connections to quasicrystals and other complex structures have been found, further expanding the scope of this work.

The complete proof and further details can be found in the linked paper.

Preprint The Universal Fractal Chirality of Riemann Zeta-Function: On...

Thank you and best regards