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

共 22 条

[1] The difference between consecutive primes, II
Baker, RC
Harman, G
Pintz, J
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2001, 83 : 532 - 562
[2] Proof of the main conjecture in Vinogradov's Mean Value Theorem for degrees higher than three
Bourgain, Jean
Demeter, Ciprian
Guth, Larry
[J]. ANNALS OF MATHEMATICS, 2016, 184 (02) : 633 - 682
[3] The asymptotic formula for localized solutions in Waring's problem and approximations to Weyl sums
Daemen, Dirk
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2010, 42 : 75 - 82
[4] The quantitative behaviour of polynomial orbits on nilmanifolds
Green, Ben
Tao, Terence
[J]. ANNALS OF MATHEMATICS, 2012, 175 (02) : 465 - 540
[5] The Mobius function is strongly orthogonal to nilsequences
Green, Ben
Tao, Terence
[J]. ANNALS OF MATHEMATICS, 2012, 175 (02) : 541 - 566
[6] Green B, 2010, ANN MATH, V171, P1753
[7] Harman G., 2007, Prime-Detecting Sieves
[8] PRIME-NUMBERS IN SHORT INTERVALS AND A GENERALIZED VAUGHAN IDENTITY
HEATHBROWN, DR
[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1982, 34 (06): : 1365 - 1377
[9] EXPONENTIAL SUMS OVER PRIMES IN SHORT INTERVALS AND AN APPLICATION TO THE WARING-GOLDBACH PROBLEM
Huang, Bingrong
[J]. MATHEMATIKA, 2016, 62 (02) : 508 - 523
[10] Strong Orthogonality between the Mobius Function and Nonlinear Exponential Functions in Short Intervals
Huang, Bingrong
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2015, 2015 (23) : 12713 - 12736

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