Sums of almost equal squares of primes

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• 作者：Angel Kumchev^a ; ^{akumchev@towson.edu} ; Taiyu Li^b ; ^{yli@mail.sdu.edu.cn}
• 关键词：primary ; 11P32 ; secondary ; 11L20 ; 11N05 ; 11N36
• 刊名：Journal of Number Theory
• 出版年：2012
• 出版时间：April 2012
• 年：2012
• 卷：132
• 期：4
• 页码：608-636
• 全文大小：302 K

文摘

We study the representations of large integers n as sums , where are primes with , for some fixed . When we use a sieve method to show that all sufficiently large integers can be represented in the above form for . This improves on earlier work by Liu, L¨¹ and Zhan (2006), who established a similar result for . We also obtain estimates for the number of integers n satisfying the necessary local conditions but lacking representations of the above form with . When our estimates improve and generalize recent results by L¨¹ and Zhai (2009), and when they appear to be first of their kind.