Maynard-Tao定理的一些应用

IF 0.4 4区数学 Q4 MATHEMATICS

American Mathematical Monthly Pub Date : 2023-03-17 DOI:10.1080/00029890.2023.2184621

Yuchen Ding, G. Zhou

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引用次数: 1

摘要

设和分别是自然数和素数的集合。对于一个正整数n，定义以下两个表示函数，Erdõs的一个旧结果表明它是无界的。作为梅纳德-陶定理的一个初步应用，我们证明了它也是无界的，这证实了陈在2010年的一个猜想。

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Some Applications of the Maynard–Tao Theorem

Abstract Let and be the set of natural numbers and prime numbers, respectively. For a positive integer n, define the following two representation functions and An old result of Erdős showed that is unbounded. As an elementary application of the Maynard–Tao theorem, we prove that is also unbounded, which confirms a conjecture of Chen in 2010.

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来源期刊

American Mathematical Monthly Mathematics-General Mathematics

CiteScore

0.80

自引率

20.00%

发文量

127

审稿时长

6-12 weeks

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