What question did this study set out to answer?

This research aims to create a framework for spectral operators in logarithmic prime lattices and explore links to the Riemann Hypothesis.

April 25, 2026Open Access

Spectral Determinants, RG Fixed Points, and Determinantal Processes (Mathematics Version)

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Key Points

This research aims to create a framework for spectral operators in logarithmic prime lattices and explore links to the Riemann Hypothesis.
Developed a rigorous framework for spectral operators defined on logarithmic prime lattices.
Analyzed the correlation hierarchy under assumptions of positivity, translation invariance, and RG stability.
Reformulated the Riemann Hypothesis using spectral conditions on a Fredholm determinant.
Identified the sine kernel as the only determinantal limit of the correlation hierarchy under the stated assumptions.
Established a spectral condition that reformulates the Riemann Hypothesis.

Abstract

We present a rigorous framework for spectral operators defined on logarithmic prime latticeswith trace-class perturbations. We establish that under positivity, translation invariance, andRG stability assumptions, the only possible determinantal limit of the correlation hierarchy isthe sine kernel. We reformulate the Riemann Hypothesis as a spectral condition on a Fredholmdeterminant.

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Oleg Glushkov

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Spectral Determinants, RG Fixed Points, and Determinantal Processes (Mathematics Version)

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