What does this research mean for the field?

A stability refinement of short-interval bounds for the Riemann zeta function yields a simple-critical zero proportion of at least 0.41907 and a distinct-zero proportion of at least 0.70953 at theta = 3/4. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

Derive a stability refinement of short-interval lower bounds for simple critical and distinct zeros of the Riemann zeta function.

September 14, 2026Open Access

A stability refinement for simple critical zeros in short intervals

View Full Paper

Ask AI

Bookmark

Derive a stability refinement of short-interval lower bounds for simple critical and distinct zeros of the Riemann zeta function.
Transferred a stability-enhanced rank-trace inequality to Lamzouri's exact finite Hilbert operator while preserving Wang's fixed-support short-interval pair-correlation hypotheses.
Applied a quantitative obstruction to additive triples of cosine-kernel zeros and evaluated the large-height limit prior to smoothing and support limits.
Generated an Arb certificate with 48,761 partition nodes and zero unresolved boxes, cross-checked using sinc Taylor evaluations at 256-bit precision.
Demonstrated a strictly positive stability refinement for every fixed exponent theta exceeding the positive-proportion threshold of the cosine bound.
Established a simple-critical zero proportion of at least 0.4190768284253039967 at theta = 3/4.
Achieved a distinct-zero proportion of at least 0.7095384142126519983 at theta = 3/4.

Discussion

No takes yet. Share an insight, caveat, or question.

Implication

Analytic study demonstrates improved lower bounds for simple critical zeros of the Riemann zeta function, suggesting tighter zero-density distributions in short intervals.

Cite This Study

Felipe Santibañez-Leal (2026) studied this question.

synapsesocial.com/papers/6aa7b3ee0926e14a848b353d https://doi.org/10.5281/zenodo.22727389

View Full Paper

Ask AI

Bookmark

Implication

Analytic study demonstrates improved lower bounds for simple critical zeros of the Riemann zeta function, suggesting tighter zero-density distributions in short intervals.

A stability refinement for simple critical zeros in short intervals

Key Points

Discussion

Implication

Cite This Study

A stability refinement for simple critical zeros in short intervals

Key Points

Discussion

Implication

Cite This Study

Also Consider

Also Consider