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ZENODO
Preprint . 2026
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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Experimental Constraints on Landau-Siegel Zeros: A 2-Billion Point Spectral Gap Analysis of Q47

Authors: Chen, Ruqing;

Experimental Constraints on Landau-Siegel Zeros: A 2-Billion Point Spectral Gap Analysis of Q47

Abstract

We present experimental constraints on hypothetical Landau-Siegel zeros derived from high-precision spectral gap analysis of the polynomial prime sequence Q(n) = n^47 - (n-1)^47. Our dataset comprises 15.4 million verified primes across the asymptotic regime n ∈ [3×10^8, 2×10^9]. TWO-STAGE VERIFICATION PROTOCOL:(1) Fast scanning algorithms for large-scale anomaly detection identified a candidate void at n ≈ 1.4×10^9(2) Arbitrary-precision verification (gmpy2) resolved this as fine-structure primes below the initial resolution threshold FINAL VERIFIED STATISTICS:- Coefficient of Variation: 0.995 (Poisson: 1.000)- Maximum Gap Ratio: 0.99 (Expected: 1.00)- Cramér Ratio: < 1.5 (Bound: 2.0)- Regional Anomalies: 0/100 CONCLUSION: No detectable perturbation from Landau-Siegel zeros within the analyzed range. The spectral gap distribution remains fully consistent with Generalized Riemann Hypothesis predictions, providing independent experimental support for GRH at the n ~ 10^9 scale. REPOSITORY CONTENTS:- Research paper (6 pages with figures)- LaTeX source- Verification figure (4-panel analysis)- Statistical results (JSON)- Analysis scripts (Python) GitHub: https://github.com/Ruqing1963/Landau-Siegel-Q47-Constraints Related publications:- Q47 Prime Dataset: DOI 10.5281/zenodo.18305185- Ouroboros Phase Transition: DOI 10.5281/zenodo.18306984

Keywords

GRH, Landau-Siegel zeros, arbitrary-precision arithmetic, prime gaps, number theory, Generalized Riemann Hypothesis, Number theory, Cramér conjecture, Poisson statistics, polynomial primes, Mathematical physics, Pure mathematics, spectral analysis

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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