What question did this study set out to answer?

The research aims to construct a Hermitian operator that approximates the non-trivial zeros of the Riemann zeta function without relying on its direct properties.

April 10, 2026Open Access

The Hilbert Pólya Operator and the Primitive Structure of the Complex Plane: Between F1, String Theory, and Ancient Geometry

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Authors

JGJorge Armando González GarcíaPolish University Abroad VGVíctor Manuel González García IPItzel Marion Dressler Pérez

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Implication

This work demonstrates an operator approximation of Riemann zeta zeros in geometry and string frameworks, suggesting geometric insights into complex analysis.

Key Points

The research aims to construct a Hermitian operator that approximates the non-trivial zeros of the Riemann zeta function without relying on its direct properties.
Constructed a Hermitian operator T* based on geometric frameworks.
Utilized a geometric-categorical structure created via the golden ratio.
Verified the framework in Lean 4 with limited axioms focused on geometric constants.
Analyzed the spectrum of the operator, with an error margin less than 1.7% across multiple orders of magnitude.
The operator's spectrum approximates 125 non-trivial zeros with high accuracy.
Three spectral invariants were derived exclusively from the geometric structure: dimension d=3, common modulus μ=1/2, and modular sum σ=3/2.
The construction is positioned within the context of F_1-descent data, contributing to advanced geometric theories.

Cite This Study

García et al. (2026) studied this question.

synapsesocial.com/papers/69d896046c1944d70ce0739e https://doi.org/10.5281/zenodo.19464695

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Implication

This work demonstrates an operator approximation of Riemann zeta zeros in geometry and string frameworks, suggesting geometric insights into complex analysis.

The Hilbert Pólya Operator and the Primitive Structure of the Complex Plane: Between F1, String Theory, and Ancient Geometry

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Implication

Key Points

Cite This Study

The Hilbert Pólya Operator and the Primitive Structure of the Complex Plane: Between F1, String Theory, and Ancient Geometry

Discussion

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Implication

Key Points

Cite This Study

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