DISTRIBUTION OF THE PRIMESREPRESENTED BY (sic)x/n(sic) IN SHORT INTERVALS

被引：0

作者：

Zhou, Guang -Liang ^{[1
]}

Feng, Ya -Fang ^{[2
]}

机构：

[1] Tongji Univ, Sch Math Sci, Shanghai, Peoples R China

[2] Nanjing Normal Univ, Sch Math Sci, Nanjing, Peoples R China

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2024年 / 54卷 / 02期

关键词：

distribution of the primes; exponential pair; the floor function; Chebyshev estimate; PRIME-NUMBERS;

D O I：

10.1216/rmj.2024.54.623

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (sic)x(sic) be the largest integer not exceeding x. For 0 < theta <= 1, let pi(theta) (x) denote the number of integers n with 1 <= n <= x(theta) such that (sic)x/n(sic) is prime. Recently, Ma, Chen and Wu obtained the interesting asymptotic formula pi(theta) (x) = x(0)/(1-theta)log x) + O(x(0) (log x)(-2)), provided that 23/47 < theta < 1. They further conjectured that this asymptotic formula can be extended to all 0 < theta < 1. In this paper, we give an improvement of their result by showing that 9/19 < theta < 1 is admissible.

引用

页码：623 / 629

页数：7