What question did this study set out to answer?

The study aims to demonstrate the unconditional convergence of the eigenvalue sequence for the Prime Gravity geodesic Schrödinger operator as the prime cutoff increases.

April 14, 2026Open Access

Spectral Convergence of the Prime Gravity Hilbert-Polya Operator

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The study aims to demonstrate the unconditional convergence of the eigenvalue sequence for the Prime Gravity geodesic Schrödinger operator as the prime cutoff increases.
Established the convergence of the Prime Gravity potential V_PG(u; W) in L²
Proved convergence of the operator family H_geo(W) to a limiting operator H_∞
Used Kato's perturbation theory to analyze eigenvalue convergence
The Prime Gravity potential converges in L² at a rate O((log W)^{−1/2})
The operator family converges to H_∞ in norm resolvent sense
Eigenvalues λ_k(W) converge to λ_k(H_∞) unconditionally

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Implication

This research proves convergence of eigenvalues in a geodesic Schrödinger operator, indicating implications for the Riemann Hypothesis.

Cite This Study

Timothy Gleason (2026) studied this question.

synapsesocial.com/papers/69ddda4de195c95cdefd7bcc https://doi.org/10.5281/zenodo.19524991

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Spectral Convergence of the Prime Gravity Hilbert-Polya Operator

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Discussion

Implication

Cite This Study

Spectral Convergence of the Prime Gravity Hilbert-Polya Operator

Key Points

Discussion

Implication

Cite This Study

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