What question did this study set out to answer?

The research aims to establish conditions under which regularized determinants related to zeta spectral triples converge uniformly, potentially supporting the Riemann Hypothesis.

June 30, 2026Open Access

Uniform Convergence of Regularized Determinants for Zeta Spectral Triples: Toward Global Weil Positivity and the Riemann Hypothesis

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The research aims to establish conditions under which regularized determinants related to zeta spectral triples converge uniformly, potentially supporting the Riemann Hypothesis.
Reorganized analytic framework for examining regularized determinants of zeta spectral triples.
Introduced criteria for convergence in a weighted topology involving minimal eigenvectors and Mellin transforms.
Demonstrated that finite determinants have real zeros based on Hurwitz’s theorem.
Establishes uniform convergence on compact subsets of the complex plane for normalized regularized determinants.
Provides a local trace theorem matching prime-power weights to the Weil explicit formula.
Indicates that convergence implies the Riemann Hypothesis through established theorems.

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Implication

Demonstrates uniform convergence of determinants in zeta spectral triples, indicating implications for the Riemann Hypothesis.

Cite This Study

Ying Ye (2026) studied this question.

synapsesocial.com/papers/6a435c8c759b888809a52eb2 https://doi.org/10.5281/zenodo.20998327

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Uniform Convergence of Regularized Determinants for Zeta Spectral Triples: Toward Global Weil Positivity and the Riemann Hypothesis

Key Points

Discussion

Implication

Cite This Study

Uniform Convergence of Regularized Determinants for Zeta Spectral Triples: Toward Global Weil Positivity and the Riemann Hypothesis

Key Points

Discussion

Implication

Cite This Study

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