哈尔滨商业大学学报（自然科学版）2023，Vol.39Issue(6)：728-731,4.
关于a21+p21=p22+p23≤x的个数问题
On number of a21 +p21 =p22 +p23≤x
摘要
Abstract
Let r1(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 r2(n)denote the number of representations of the positive integer n as the sum of the squares of two prime numbers.Use S1,2(x)torepresentthemeanvalues∑n≤xr1(n)r2(n).Sedunova calculated x/log2x≪ S1,2(x)≪ x/log2x(loglogx)2.In this paper,the Brun sieve was used to further x improve this result.Proved that when there was x→∞,there was S1,2(x)(())x/log2x.关键词
平方和/算术级数中的素数/格点计数/Brun筛法Key words
sum of squares/primes in arithmetic progressions/lattice counting/Brun sieve分类
数理科学引用本文复制引用
张悦,戴浩波..关于a21+p21=p22+p23≤x的个数问题[J].哈尔滨商业大学学报（自然科学版）,2023,39(6):728-731,4.基金项目
国家自然科学基金(11501007). （11501007）
