Selberg Trace Formula Links Hyperbolic Geodesics to GUE Random Matrix Theory — E8 Intelligence Research

Andrew Stewart Caldin

doi:10.5281/zenodo.21697908

July 30, 2026Open Access

Selberg Trace Formula Links Hyperbolic Geodesics to GUE Random Matrix Theory — E8 Intelligence Research

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Key Points

This research aims to explore the relationship between spectral statistics of Laplacians on hyperbolic surfaces and GUE random matrix theory.
Utilized Selberg trace formula to analyze connections between prime geodesic lengths and Riemann zeta zeros.
Examined the nearest-neighbor distribution of GUE eigenvalues in relation to hyperbolic geometry and quantum chaos.
Explored the Selberg and Riemann zeta functions to uncover their interconnections with number theory.
Identified a link between hyperbolic geodesic lengths and log(p^m) for primes, enhancing understanding of prime distribution.
Showed that GUE eigenvalue spacing mirrors the distribution of Riemann zeta zeros, reflecting a golden ratio pattern.
Demonstrated that Selberg zeta function aligns with Euler product, reinforcing the connection between number theory and quantum physics.

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Implication

Mathematical findings uncover connections between spectral statistics and prime geodesics, indicating profound links between number theory and quantum physics.

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Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a6d9885e258b358b3c6c027 https://doi.org/10.5281/zenodo.21697908

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Selberg Trace Formula Links Hyperbolic Geodesics to GUE Random Matrix Theory — E8 Intelligence Research

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Selberg Trace Formula Links Hyperbolic Geodesics to GUE Random Matrix Theory — E8 Intelligence Research

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