Sums of almost equal squares of primes

JOURNAL OF NUMBER THEORY

卷:132

Article

Kumchev, Angel¹  Li, Taiyu² 

[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 squares;    Exceptional sets;    Distribution of primes;    Sieve methods;    Exponential sums;   

DOI  :  10.1016/j.jnt.2011.12.004

来源: Elsevier

【 摘 要 】

We study the representations of large integers n as sums p(1)(2) + ... + p(s)(2) where p(1), ...., p(s) are primes with |p(i) - (n/s)(1/2)| <= n(0/2), for some fixed theta < 1. When s = 5 we use a sieve method to show that all sufficiently large integers n 5 (mod 24) can be represented in the above form for theta > 8/9. This improves on earlier work by Liu, Lu and Zhan (2006), who established a similar result for theta > 9/10. We also obtain estimates for the number of integers n satisfying the necessary local conditions but lacking representations of the above form with s = 3,4. When s = 4 our estimates improve and generalize recent results by Lu and Zhai (2009), and when s =3 they appear to be first of their kind. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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