On sums of powers of almost equal primes

JOURNAL OF NUMBER THEORY

卷:176

Article

Kumchev, Angel¹  Liu, Huafeng² 

[1] Towson Univ, Dept Math, Towson, MD 21252 USA

[2] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

关键词: Waring-Goldbach problem;    Almost equal primes;    Primes in short intervals;    Sieve methods;    Circle method;   

DOI  :  10.1016/j.jnt.2016.12.003

来源: Elsevier

【 摘 要 】

Let k >= 2 ands be positive integers, and let n be a large positive integer subject to certain local conditions. We prove that if s >= k(2) + k + 1 and 0 > 31/40, then n can be expressed as a sum p(1)(k) +...+p(s)(k) where p(1,)...,p(s) are primes with broken vertical bar p(j) - (n/s)(1/k)broken vertical bar <= n(theta/k). This improves on earlier work by Wei and Wooley [15] and by Huang [8] who proved similar theorems when theta > 19/24. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free