Work

Alfredo Luis Acosta Padilla

Year: 2025

Type: article

Abstract: We refine the constant tracking in the Hardy-Littlewood circle method so that the binary Goldbach conjecture is reduced to the interval 4 ≤ n ≤ 2.0 × 10¹⁹. Our two principal ingredients are: A) A point-wise minor-arc bound |S(α)| ≤ 1.2 n/(log n)¹² obtained via an L²-Bessel estimate, an improved inverse large sieve, and the choice y = n^0.32 in Vaughan's identity. B) A fully explicit major-arc evaluation. The constants are tabulated and every inequality is justified in the appendices, allowing an independent audit. Only 1.6 × 10¹⁹ even integers remain to be checked by computer.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.16106592

Author: ALFREDO LUIS, ACOSTA PADILLA

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6949883841

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