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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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Overview

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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