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This note aims to measure the gap-ratio statistic of the non-trivial zeros of the Riemann zeta function and identify the peak candidates.

May 17, 2026Open Access

An Empirical Note on the Riemann Zero Gap-Ratio Peak

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Empirical note measures gap-ratio statistics in Riemann zeta function zeros, highlighting peak candidates.

This note aims to measure the gap-ratio statistic of the non-trivial zeros of the Riemann zeta function and identify the peak candidates.
Analyzed four Odlyzko zero datasets from gamma approximately 7.5 x 10^4 to gamma approximately 1.4 x 10^21.
Used both restricted and unrestricted gap-ratio definitions after standard local unfolding.
Conducted a 10,000-resample bootstrap analysis on the highest-T dataset (zeros5).
Eliminated ln 2 as the closest anchor with 0.38% share for unrestricted and 0.26% for restricted.
1/phi emerged as the closest anchor for both statistics, achieving 94.93% share at gamma approximately 10^21.
In the restricted statistic, empirical KDE density was higher at 1/sqrt(2) compared to 1/phi.

Ryan W. Yett (2026) studied this question.

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May 17, 2026Open Access

View Full Paper

Ask AI

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Authors

Empirical note measures gap-ratio statistics in Riemann zeta function zeros, highlighting peak candidates.

This note aims to measure the gap-ratio statistic of the non-trivial zeros of the Riemann zeta function and identify the peak candidates.
Analyzed four Odlyzko zero datasets from gamma approximately 7.5 x 10^4 to gamma approximately 1.4 x 10^21.
Used both restricted and unrestricted gap-ratio definitions after standard local unfolding.
Conducted a 10,000-resample bootstrap analysis on the highest-T dataset (zeros5).
Eliminated ln 2 as the closest anchor with 0.38% share for unrestricted and 0.26% for restricted.
1/phi emerged as the closest anchor for both statistics, achieving 94.93% share at gamma approximately 10^21.
In the restricted statistic, empirical KDE density was higher at 1/sqrt(2) compared to 1/phi.

Ryan W. Yett (2026) studied this question.

View Full Paper

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