On certain inequalities for the prime counting function-Part III

被引：3
|
作者：
Sandor, Jozsef [1 ]
机构：
[1] Babes Bolyai Univ Cluj Napoca, Dept Math, Cluj Napoca, Romania
来源：
NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS | 2023年 / 29卷 / 03期
关键词：
Prime counting function; Inequalities; Hardy-Littlewood conjecture; Landau's inequality; Prime numbers;
D O I：
10.7546/nntdm.2023.29.3.454
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
As a continuation of [10] and [11], we offer some new inequalities for the prime counting function 7r(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 7r(p2n) are offered, pn denoting the n-th prime number. Results on 7r(7r(x)) are also considered.
引用
收藏
页码：454 / 461
页数：8
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