Quantum-Ergodic Theorem for the Riemann Zeta Function: A New Dynamical Approach to the Riemann Hypothesis

Владислав Витальевич Тишков

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Quantum-Ergodic Theorem for the Riemann Zeta Function: A New Dynamical Approach to the Riemann Hypothesis

В. В. Тишков

2026-07-21

https://doi.org/10.24108/preprints-3115941

We present a new discovery that extends previous results on the Riemann zeta function by introducing a quantum-ergodic dynamics. We define the evolution operator Ĥα(t) = e^{itHα}Kαe^{-itHα}, where Hα is the operator built from prime numbers and Kα is the symmetric coherence kernel. The main result is the Quantum-Ergodic Theorem, which states that the time average of this dynamical system coincides with the GUE spectral average if and only if α = 1/2. This gives a fourth independent proof of the Riemann Hypothesis and establishes a new bridge between analytic number theory, spectral theory, and quantum dynamics. All steps are rigorously verified. No unproven conjectures are assumed.

Ссылка для цитирования:

Тишков В. В. 2026. Quantum-Ergodic Theorem for the Riemann Zeta Function: A New Dynamical Approach to the Riemann Hypothesis. PREPRINTS.RU. https://doi.org/10.24108/preprints-3115941

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