What question did this study set out to answer?

The aim is to create a functor that links the spectral gap of an operator to pair correlation bounds.

March 27, 2026Open Access

Spectral Completeness Functor From Operator Gap to Pair Correlation via Weil Positivity on the √2-Weighted Space

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Mathematical construction translates spectral properties into bounds on pair correlation, suggesting connections for the Riemann hypothesis.

The aim is to create a functor that links the spectral gap of an operator to pair correlation bounds.
Constructed a functor that translates spectral gaps into correlation criteria.
Analyzed the spectral properties of arithmetic operators on the torus.
Investigated zero statistics of the Riemann zeta function.
Establishes a connection between spectral theory and zero distribution.
Provides bounds on the Montgomery pair correlation function based on spectral gaps.

Thierry Marechal (2026) studied this question.

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March 27, 2026Open Access

View Full Paper

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Authors

Mathematical construction translates spectral properties into bounds on pair correlation, suggesting connections for the Riemann hypothesis.

The aim is to create a functor that links the spectral gap of an operator to pair correlation bounds.
Constructed a functor that translates spectral gaps into correlation criteria.
Analyzed the spectral properties of arithmetic operators on the torus.
Investigated zero statistics of the Riemann zeta function.
Establishes a connection between spectral theory and zero distribution.
Provides bounds on the Montgomery pair correlation function based on spectral gaps.

Thierry Marechal (2026) studied this question.

View Full Paper

Ask AI

Bookmark