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This research aims to create a functional-analytic framework for representing Dirichlet energy related to the Riemann zeta function as a Hilbert operator.

April 27, 2026Open Access

The Riemann Hypothesis: A Hilbert Operator

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This research aims to create a functional-analytic framework for representing Dirichlet energy related to the Riemann zeta function as a Hilbert operator.
Developed a self-adjoint operator on a separable Hilbert space using a hyperbolic kernel.
Utilized a Toeplitz-type quadratic form and established finite-dimensional truncations.
Employed Bochner-type arguments to ensure positivity in the kernel and connect to number theory.
Constructed a compact operator that is spectrally stable and well-defined.
Showed the positivity of the quadratic form links to the Riemann Hypothesis, under explicit-formula assumptions.
Achieved rapid convergence in numerical stability checks and spectral diagnostics.

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Implication

Functional-analytic framework encodes energy and establishes a model for the Riemann Hypothesis.

Cite This Study

Jason Mullings (2026) studied this question.

synapsesocial.com/papers/69eefdb5fede9185760d46a3 https://doi.org/10.5281/zenodo.19748413

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The Riemann Hypothesis: A Hilbert Operator

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Implication

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The Riemann Hypothesis: A Hilbert Operator

Key Points

Discussion

Implication

Cite This Study

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