关于a_(1)^(2)+p_(1)^(2)=p_(2)^(2)+p_(3)^(2)≤x的个数问题  

On number of a_(1)^(2)+p_(1)^(2)=p_(2)^(2)+p_(3)^(2)≤x

作　　者：张悦 戴浩波 ZHANG Yue;DAI Haobo(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan 232001,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232001

出　　处：《哈尔滨商业大学学报（自然科学版）》2023年第6期728-731,共4页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：国家自然科学基金(11501007).

摘　　要：记r_(1)(n)为可以表示成一个正整数与一个素数的平方和的正整数n的个数,记r_(2)(n)为可以表示成两个素数平方和的正整数n的个数.用S_(1,2)(x)表示均值∑n≤xr_(1)(n)r_(2)(n).Sedunova计算得出x/log^(2)xS_(1,2)(x)x/log^(2)x(loglogx)^(2).利用Brun筛法进一步完善此结果.证明当x→∞时,有S_(1,2)(x)■x/log^(2)x.Let r_(1)(n)denote the number of representations of the positive integer n as the sum of a square of a positive integer and the square of a positive prime number,let r_(2)(n)denote the number of representations of the positive integer n as the sum of the squares of two prime numbers.Use S_(1,2)(x)to represent the mean values∑_(n≤x)r_(1)(n)r_(2)(n).Sedunova calculated x/log^(2)xS_(1,2)(x)x/log^(2)x(loglogx)^(2).In this paper,the Brun sieve was used to further improve this result.Proved that when there was x→∞,there was S_(1,2)(x)■x/log^(2)x.

关 键 词：平方和 算术级数中的素数 格点计数 Brun筛法 

分 类 号：O156[理学—数学]