What does this research mean for the field?

The application of odd-multiplicity parity and odd-frame pressure transfers to the finite stable Hilbert rank-trace method yields specific lower bounds for the proportions of simple and distinct nontrivial zeros of the Riemann zeta function in short intervals, including a simple-critical lower bound of approximately 0.419 at theta=3/4. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

Quantify lower bounds for the proportions of simple and distinct nontrivial zeros of the Riemann zeta function located on the critical line in short intervals.

September 14, 2026Open Access

Simple critical zeros in short intervals: stability, pressure, and parity

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Quantify lower bounds for the proportions of simple and distinct nontrivial zeros of the Riemann zeta function located on the critical line in short intervals.
Applied the finite stable Hilbert rank-trace framework combined with Wang's fixed-test short-interval setup.
Integrated an odd-multiplicity parity transfer with an odd-frame pressure transfer via a certified two-variable interval certificate across 16,797 nodes.
Established a simple-critical lower bound of max{0, c(theta), (c(theta)+2 kappa)/3} for any fixed exponent theta in (0.51, 1), guaranteeing positive simple-critical density below Wang's cosine positivity root.
Certified a simple-critical zero lower bound of 0.419087888170111727959091183775 and a distinct companion proportion of 0.709543944085055863979545591888 at theta = 3/4.

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Implication

Theoretical analysis reveals lower bounds on simple and distinct zeros in short intervals of the Riemann zeta function, highlighting improved critical-line density estimates.

Cite This Study

Felipe Santibañez-Leal (2026) studied this question.

synapsesocial.com/papers/6aa7b3aa0926e14a848b2bb0 https://doi.org/10.5281/zenodo.22727388

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Implication

Theoretical analysis reveals lower bounds on simple and distinct zeros in short intervals of the Riemann zeta function, highlighting improved critical-line density estimates.

Simple critical zeros in short intervals: stability, pressure, and parity

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Implication

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Simple critical zeros in short intervals: stability, pressure, and parity

Key Points

Discussion

Implication

Cite This Study

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