A note on the Cramér–Granville model

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2026-01-27 DOI:10.1007/s00013-025-02214-x

Christian Táfula

引用次数: 0

Abstract

We show the existence of a set $A\subseteq \mathbb {Z}_{\ge 2}$ satisfying the estimates of the Bateman–Horn conjecture, Goldbach’s conjecture, and also

$$\begin{aligned} \#\{p\le x \text { prime} ~|~ p\in A\} \gg x(\log \log x)/(\log x)^2. \end{aligned}$$

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关于cramsamr - granville模型的注释

我们证明了一个集$A\subseteq \mathbb {Z}_{\ge 2}$的存在性，该集满足Bateman-Horn猜想、Goldbach猜想和also的估计 $$\begin{aligned} \#\{p\le x \text { prime} ~|~ p\in A\} \gg x(\log \log x)/(\log x)^2. \end{aligned}$$

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.