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April 25, 2026Open Access

Unified Spectral RG Framework for the Riemann Zeta Function and Random Matrix Theory

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Authors

OGOleg Glushkov

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Implication

Randomized trial connects prime Hamiltonians and Riemann zeta function, suggesting a new approach to spectral uniqueness.

Key Points

  • This research aims to establish a unified spectral framework linking prime Hamiltonians with the Riemann zeta function and random matrix theory.
  • Constructed trace-class perturbations of diagonal prime operators.
  • Utilized Fredholm spectral determinants and RG flow of correlation kernels.
  • Analyzed fixed-point conditions to establish universality in correlation hierarchies.
  • Demonstrated that the sine-kernel determinantal process uniquely corresponds to the Gaussian Unitary Ensemble (GUE) under specific conditions.
  • Reformulated the Riemann Hypothesis as a spectral uniqueness criterion for RG-stable determinant classes.

Cite This Study

Oleg Glushkov (2026) studied this question.

synapsesocial.com/papers/69ec5b0688ba6daa22dac930https://doi.org/10.5281/zenodo.19708238
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Spectral Determinants, RG Flow, and GUE Universality (Physics Version)2026
  2. 2Spectral Determinants, RG Fixed Points, and Determinantal Processes (Mathematics Version)2026
  3. 3A Proposed RG–Spectral Framework for the Stability of the Critical Line via Prime Variance Invariance2026
  4. 4Structural Universality and the Critical Line: A Stability Criterion for Spectral Realizations of the Zeta Function2026
  5. 5A Unified Spectral-Equilibrium Proof of the Riemann Hypothesis via the Spectral-Unitary Framework (SUF)2026