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May 8, 2026Open Access

Numerical Exploration of Minor Arc Energy in the Binary Goldbach Problem

Key Points

This research aims to explore the distribution of minor-arc energy in the binary Goldbach problem using numerical methods.
Investigated the distribution of minor-arc energy using weighted exponential sums involving the von Mangoldt function.
Introduced a danger-score framework to assess proximity to low-complexity rationals.
Conducted computations up to N=128000 to analyze cumulative distributions based on rescaled danger levels.
Minor-arc energy is predominantly distributed in low-danger regions.
Rescaling the danger threshold by (log⁡N)^2 led to the best empirical fit for cumulative distributions.

Abstract

This preprint numerically investigates the distribution of minor-arc energy in the binary Goldbach problem using weighted exponential sums involving the von Mangoldt function. It introduces a danger-score framework to measure arithmetic proximity to low-complexity rationals and studies how minor-arc energy is distributed across different danger levels. The computations suggest that minor-arc energy is strongly concentrated in low-danger regions and that rescaling the danger threshold by (log⁡N) ², gives the best empirical collapse of the cumulative distributions over the tested range, up to N=128000.

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Authors

Dimitrios Dimitrios Morakis

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Democritus University of Thrace

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Numerical Exploration of Minor Arc Energy in the Binary Goldbach Problem

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Authors

Actions

Institutions

References and Citations

Citation Network

Connected Papers

Discussion

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