What question did this study set out to answer?

The aim is to construct a self-adjoint operator that numerically aligns with the properties of Hilbert–Pólya candidates associated with Riemann zeros.

April 28, 2026Open Access

The Riemann Hypothesis: A Hilbert–Pólya Candidate Operator.

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The aim is to construct a self-adjoint operator that numerically aligns with the properties of Hilbert–Pólya candidates associated with Riemann zeros.
Developed a finite-dimensional, self-adjoint operator composed of multiple components including an arithmetic diagonal and resonance-tuned kernel.
Added a small Gaussian perturbation for chaotic statistics and ensured exact spectral symmetry in the operator.
Validated results numerically for dimensions up to two thousand.
The operator is exactly self-adjoint with real eigenvalues.
Eigenvalue counting functions closely align with Riemann–von Mangoldt density within 1% error.
Eigenvalue spacings reflect Wigner-GUE statistics, confirming similarities with Riemann data.

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Implication

This research presents a model using a self-adjoint operator to analyze the Riemann zeros, suggesting a possible framework for Riemann Hypothesis testing.

Cite This Study

Jason Mullings (2026) studied this question.

synapsesocial.com/papers/69f04e5b727298f751e724c7 https://doi.org/10.5281/zenodo.19794442

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Implication

This research presents a model using a self-adjoint operator to analyze the Riemann zeros, suggesting a possible framework for Riemann Hypothesis testing.

The Riemann Hypothesis: A Hilbert–Pólya Candidate Operator.

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Discussion

Implication

Cite This Study

The Riemann Hypothesis: A Hilbert–Pólya Candidate Operator.

Key Points

Discussion

Implication

Cite This Study

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