The estimate for mean values on prime numbers relative to 4/p=1/(n_1) + 1/(n_2) + 1/(n_3)

作     者：JIA ChaoHua 1,2 1 Institute of Mathematics,Chinese Academy of Sciences,Beijing 100190,China 2 Hua Loo-Keng Key Laboratory of Mathematics,Chinese Academy of Sciences,Beijing 100190,China 

作者机构：Institute of Mathematics Chinese Academy of Sciences Beijing 100190 China Hua Loo-Keng Key Laboratory of Mathematics Chinese Academy of Sciences Beijing 100190 China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2012年第55卷第12期

页      面：465-474页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by National Natural Science Foundation of China (Grant No.11071235) 

主　　题：Diophantine equation prime number mean value 

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_*** 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 *** this paper,we shall study the estimate for mean values ∑ px f i (p),i=1,2,where p denotes the prime number.