关于 Hardy-Littlewood 推广 Goldbach 猜想的一个初等启发式方法
数论
2024-12-18 v5 组合数学
摘要
本文的目标是描述一个初等的组合启发式方法，该方法预测了 Hardy 和 Littlewood 推广的 Goldbach 猜想。我们考察了加性素数理论中其他启发式方法的共同特征，例如 Cramér 模型和密度型论证，我们的启发式方法借鉴了这两者。除了素数定理外，我们的论证完全是初等的，即不涉及复分析。其核心思想是用超几何概率分布对两个素数之和进行建模，然后从其集中行为中得出启发式结论，该集中行为源自 Hoeffding 型界。
引用
@article{arxiv.1508.05702,
title = {An elementary heuristic for Hardy-Littlewood extended Goldbach's conjecture},
author = {Christian Táfula},
journal= {arXiv preprint arXiv:1508.05702},
year = {2024}
}
备注
13 pages, 3 figures. The old version of this article ([v1], [v2]) has been expanded and split into two separate papers: arXiv:1807.10200 and the present one. From [v3], [v4] to this version: grammar was corrected, references were added, and figures were adjusted. For the scripts used to generate the figures, see https://github.com/tafula/hl_ext_gb_conj