On the singular series for primes in arithmetic progressions

被引：1

作者：

Ge, Wenxu ^{[1
]}

Liu, Huake ^{[1
]}

机构：

[1] North China Univ Water Resources & Elect Power, Sch Math & Informat Sci, Zhengzhou 450046, Henan, Peoples R China

来源：

LITHUANIAN MATHEMATICAL JOURNAL | 2017年 / 57卷 / 03期

基金：

中国国家自然科学基金;

关键词：

singular series; prime pair problem; Goldbach problem; arithmetic progressions; Hardy-Littlewood conjecture; GOLDBACH NUMBERS; SHORT INTERVALS;

D O I：

10.1007/s10986-017-9362-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using (d, k) to denote the singular series for primes in arithmetic progressions and using the word "tail" to denote the difference of (d, k) and its partial sums, we establish some asymptotic formulas for weighted sums of the square of the tail and so give more information on the singular series (d, k).

引用

页码：294 / 318

页数：25

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