关于质数计数函数的某些不等式 - 第三部分

IF 0.4 Q4 MATHEMATICS Notes on Number Theory and Discrete Mathematics Pub Date : 2023-07-03 DOI:10.7546/nntdm.2023.29.3.454-461

József Sándor

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引用次数: 0

摘要

作为 [10] 和 [11] 的继续，我们为素数计数函数 $\pi (x) $ 提供了一些新的不等式，特别是提供了哈代-利特尔伍德猜想的乘法类比。还给出了朗道不等式的逆向改进。提供了一些关于 $\pi (p_n^2)$ 的结果，$p_n$ 表示第 $n$ 个素数。还考虑了关于 $\pi (\pi (x))$ 的结果。

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On certain inequalities for the prime counting function – Part III

As a continuation of [10] and [11], we offer some new inequalities for the prime counting function $\pi (x).$ Particularly, a multiplicative analogue of the Hardy–Littlewood conjecture is provided. Improvements of the converse of Landau's inequality are given. Some results on $\pi (p_n^2)$ are offered, $p_n$ denoting the $n$-th prime number. Results on $\pi (\pi (x))$ are also considered.

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Notes on Number Theory and Discrete Mathematics MATHEMATICS-

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33.30%

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