Distribution of integers that are sums of three squares of primes
Distribution of integers that are sums of three squares of primes
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DOI：
10.4064/aa98-3-1
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发表时间：
2001
期刊：
影响因子：
0.7
通讯作者：
Jianya Liu;T. Zhan
中科院分区：
文献类型：
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作者：
Jianya Liu;T. Zhan
(1.1)n=p1+p2 2+p2 3.更精确地说，设H={n≥1：n≡3(Mod 2 4)，n 6≡0(Mod 5)}，E(N)是不能表示为(1.1)的n∈H的个数.后来，−[16]证明了华氏估计对任意的A>；0成立。1993年，梁和刘[10]将E(N)的上界改进为N1−δ，其中δ>；0是某种可计算的绝对常数，其中取决于杜林-海尔布伦现象中的常数。最近，Bauer，Liu和詹[1]用一种不同的方法处理了这个问题，没有杜林-海尔布伦现象，并建立了E(N)N 77/80+ε，其中ε>；0是任意的。在本文中，我们做了以下改进。
(1.1) n = p1 + p 2 2 + p 2 3. To be more precise, let H = {n ≥ 1 : n ≡ 3 (mod 24), n 6≡ 0 (mod 5)}, and let E(N) be the number of n ∈ H not exceeding N that cannot be represented as (1.1). Then Hua’s result actually states that E(N) N log−AN for some positive constant A. Later Schwarz [16] proved that Hua’s estimate holds for arbitrary A > 0. And in 1993, Leung and Liu [10] improved the upper bound of E(N) to N1−δ, where δ > 0 is some computable absolute constant depending on, among other things, the constants in the Deuring– Heilbronn phenomenon. Recently, Bauer, Liu, and Zhan [1] have dealt with this problem via a different approach without the Deuring–Heilbronn phenomenon, and established E(N) N 77/80+ε, where ε > 0 is arbitrary. In this paper, we make the following improvement.