Exponential sums over primes in short intervals

被引：13

作者：

Liu Jianya ^{[1
]}

Lu Guangshi ^{[1
]}

Zhan Tao ^{[1
]}

机构：

[1] Shandong Univ, Dept Math, Jinan 250100, Peoples R China

来源：

SCIENCE IN CHINA SERIES A-MATHEMATICS | 2006年 / 49卷 / 05期

关键词：

exponential sums over primes; circle method; Waring-Goldbach problems;

D O I：

10.1007/s11425-006-0611-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we establish one new estimate on exponential sums over primes in short intervals. As an application of this result, we sharpen Hua's result by proving that each sufficiently large integer N congruent to 5 modulo 24 can be written as N = p(1)(2) + P-2(2) + P-3(2) + P-4(2) + P-5(2), with vertical bar pj - root N/5 vertical bar <= U = N1/2 - 1/20 + epsilon, where pj are primes. This result is as good as what one can obtain from the generalized Riemann hypothesis.

引用

页码：611 / 619

页数：9

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