The estimate for mean values on prime numbers relative to 4/p=1/n1+1/n2+1/n3

被引：0

作者：

Jia ChaoHua ^{[1
,2
]}

机构：

[1] Chinese Acad Sci, Inst Math, Beijing 100190, Peoples R China

[2] Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2012年 / 55卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Diophantine equation; prime number; mean value;

D O I：

10.1007/s11425-011-4348-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

If n is a positive integer, let f(n) denote the number of positive integer solutions (n (1), n (2), n (3)) of the Diophantine equation 4/n = 1/n(1) + 1/n(2) + 1/n(3) For the prime number p, f(p) can be split into f (1)(p) + f (2)(p), where f (i) (p) (i = 1, 2) counts those solutions with exactly i of denominators n (1), n (2), n (3) divisible by p. In this paper, we shall study the estimate for mean values Sigma(p<x) f(i)(p), i = 1,2, where p denotes the prime number.

引用

页码：465 / 474

页数：10