关于偏移素数及筛集的 Hardy-Ramanujan 型不等式
数论
2022-07-05 v3
摘要
我们建立了 Hardy-Ramanujan 不等式的一个类比，用于计数具有给定个不同素因子数的筛集元素。特别地，我们对小于 x 且带有 k 个不同素因子的偏移素数 p+a 的数量给出了一个一致于所有正整数 k 的估计。
关键词
引用
@article{arxiv.2101.03440,
title = {A Hardy-Ramanujan type inequality for shifted primes and sifted sets},
author = {Kevin Ford},
journal= {arXiv preprint arXiv:2101.03440},
year = {2022}
}
备注
v3. Added hypothesis x>2|a| to Cor. 1 and 3; changed hypothesis in Theorem 1 so that s is ANY pos. integer dividing all members of S (this is needed for Cor. 1 and Cor. 3). Added remarks explaining that gcd{p+a:p+a in Q(E)} is not always 1 or 2