Discorrelation Between Primes in Short Intervals and Polynomial Phases

被引：5

作者：

Matomaki, Kaisa ^{[1
]}

Shao, Xuancheng ^{[2
]}

机构：

[1] Univ Turku, Dept Math & Stat, Turku 20014, Finland

[2] Univ Kentucky, Dept Math, Lexington, KY 40506 USA

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2021年 / 2021卷 / 16期

基金：

芬兰科学院; 美国国家科学基金会;

关键词：

THEOREM; DIFFERENCE;

D O I：

10.1093/imrn/rnz188

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let H = N-theta, theta > 2/3 and k >= 1. We obtain estimates for the following exponential sum over primes in short intervals: Sigma(N<n <= N+H) Lambda(n)e(g(n)), where g is a polynomial of degree k. As a consequence of this in the special case g(n) = alpha n(k), we deduce a short interval version of the Waring-Goldbach problem.

引用

页码：12330 / 12355

页数：26