Working Hypothesis: "Zeta Function Resonance Grid" Riemann Hypothesis
We propose a wave-based physical interpretation of the Riemann Hypothesis by modeling the zeta function as a standing wave in logarithmic space. We show that the sum of complex waveforms of the form ψ_t(x) = x^{-1/2 + it}, where t is the imaginary part of a nontrivial zero of ζ(1/2 + it), forms an interference structure with annihilation points. We introduce a self-adjoint operator H whose spectrum potentially matches the imaginary parts of the Riemann zeta function’s nontrivial zeros. An AI model was trained to detect annihilation regions based on local wave patterns, achieving 100% accuracy on both real and synthetic tests. The model distinguishes genuine zeta zeros from artificially shifted frequencies and anticipates zero-like behavior even in narrow intervals. This approach could lay the foundation for a spectral proof of the Riemann Hypothesis.
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2025-04-03
- DOI
- https://doi.org/10.5281/zenodo.15127997
- Primary Topic
- Analytic Number Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00