共查询到10条相似文献,搜索用时 78 毫秒
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REN Xiumin Department of Mathematics Shandong University Jinan China 《中国科学A辑(英文版)》2005,48(6):785-797
In this paper, we prove the following estimate on exponential sums over primes: Let κ≥1,βκ=1/2 log κ/log2, x≥2 and α=a/q λsubject to (a, q) = 1, 1≤a≤q, and λ∈R. Then As an application, we prove that with at most O(N2/8 ε) exceptions, all positive integers up to N satisfying some necessary congruence conditions are the sum of three squares of primes. This result is as strong as what has previously been established under the generalized Riemann hypothesis. 相似文献
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On sums of a prime and four prime squares in short intervals 总被引:1,自引:1,他引:0
In this paper, we prove that each sufficiently large integer N ≠1(mod 3) can be written as N=p+p1^2+p2^2+p3^2+p4^2, with
|p-N/5|≤U,|pj-√N/5|≤U,j=1,2,3,4,
where U=N^2/20+c and p,pj are primes. 相似文献
|p-N/5|≤U,|pj-√N/5|≤U,j=1,2,3,4,
where U=N^2/20+c and p,pj are primes. 相似文献
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设A(n)为von Mangoldt函数且实数θ=95-83~(1/2)/121.当xθ+ε≤y≤x时,本文对于所有的α∈[0,1]给出了指数和S2(x,y;α)=∑x0,估计式∑x相似文献
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Let c>1 and : We study the solubility of the Diophantine inequality in Piatetski-Shapiro primes p1,p2, .., ps of the form for some , and improve the previous results in the cases s = 2, 3, 4. 相似文献
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研究了把一个满足必要条件的自然数在小区间内分解成一个素数和三个素数平方和的问题,利用刘建亚和展涛处理扩大了的主区间的新方法,成功的缩短了小区间的长度. 相似文献
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We give explicit upper bounds for linear trigonometric sums over primes.
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Hui Xue Lao 《数学学报(英文版)》2009,25(4):687-692
Let Af(n) be the coefficient of the logarithmic derivative for the Hecke L-function. In this paper we study the cancellation of the function Ay(n) twisted with an additive character e(α√n), α 〉0, i.e. Ef(x) = Σx〈n〈2x Af(n)e(α√n). 相似文献