Exponential sums over primes in short intervals

被引：2
|
作者：
Huang, Bingrong [1 ]
Wang, Zhiwei [1 ]
机构：
[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China
来源：
JOURNAL OF NUMBER THEORY | 2015年 / 148卷
关键词：
Exponential sums; von Mangoldt function; Short intervals;
D O I：
10.1016/j.jnt.2014.09.004
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let Lambda(n) be the von Mangoldt function, x real and 2 <= y <= x. This paper improves the estimate on the exponential sum over primes in short intervals S-k(x, y; alpha) = Sigma Lambda(n)e(n(k)alpha) x<n <= x+y when k >= 4 for all alpha is an element of [0,1]. And then combined with the Hardy-Littlewood method, this enables us to give some short interval variants of Hua's theorems in additive prime number theory. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：204 / 219
页数：16
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