共查询到20条相似文献,搜索用时 0 毫秒
1.
Guangshi Lü 《Journal of Number Theory》2008,128(4):805-819
In this paper, we are able to sharpen Hua's classical result by showing that each sufficiently large integer can be written as
2.
On sums of a prime and four prime squares in short intervals 总被引:1,自引:0,他引:1
Xian-Meng Meng 《Acta Mathematica Hungarica》2004,105(4):261-283
3.
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
4.
Richard H. Hudson 《manuscripta mathematica》1983,42(2-3):285-288
Bounds for the second and third smallestprime k-th power nonresidues of odd primes p have been given by Alfred Brauer, Clifton Whyburn, and L. K. Hua. Bounds for the n-th prime residue, n≥4, do not appear in the literature and it would be difficult to obtain bounds as sharp as p1/4 if n is large and k is small. In this note we use the character sum estimates of D. A. Burgess to show that there are on the order of log p/log log pprime k-th power nonresidues less than p1/4 +∈ for every ∈>0 and sufficiently large p. 相似文献
5.
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
6.
N. N. Mot’kina 《Mathematical Notes》2006,79(5-6):848-853
Suppose that the Riemann hypothesis holds. Suppose that $$\psi _1 (x) = \mathop \sum \limits_{\begin{array}{*{20}c} {n \leqslant x} \\ {\{ (1/2)n^{1/c} \} < 1/2} \\ \end{array} } \Lambda (n)$$ where c is a real number, 1 < c ≤ 2. We prove that, for H>N 1/2+10ε, ε > 0, the following asymptotic formula is valid: $$\psi _1 (N + H) - \psi _1 (N) = \frac{H}{2}\left( {1 + O\left( {\frac{1}{{N^\varepsilon }}} \right)} \right)$$ . 相似文献
7.
The Ramanujan Journal - Let d(n) denote the Dirichlet divisor function. Define $$begin{aligned} mathcal {S}_k(x,y):= sum _{begin{array}{c} x-y 相似文献
8.
设k≥2,且Hk表示一个正整数n的集合,使得该集合中的元素满足a+bk≡n(modq)对任意的q,在模q的既约剩余系中有解,令Dk(N)表示所有的n≤N,且n∈Hk且不能表成p1+p2k=n形式的整数.那么在GRH下, Dk(N)相似文献
9.
Under the assumption of the Riemann hypothesis the
asymptotic value y/log x is known to hold for the number of
primes in the short interval [x - y, x] for
for
every fixed
.
We show under the assumption
of the existence of exceptional Dirichlet characters the same
asymptotic formula holds in the shorter intervals, for some
\, in wide ranges of x depending on the
characters. 相似文献
10.
The main purpose of this paper is to study the mean value properties of a sum analogous to character sums over short intervals
by using the mean value theorems for the Dirichlet L-functions, and to give some interesting asymptotic formulae.
This work is supported by the N.S.F. (60472068) of P.R. China. 相似文献
11.
Adrian W. Dudek 《The Ramanujan Journal》2017,42(1):233-240
We prove that every integer greater than two may be written as the sum of a prime and a square-free number. 相似文献
12.
Archiv der Mathematik - 相似文献
13.
14.
Using the Karatsuba method, we obtain new estimates for Kloosterman sums modulo a prime, which, under certain constraints on the number of summands, are sharper than similar estimates found earlier.
相似文献15.
Under the Riemann hypothesis and the conjecture that the order of growth of the argument of ζ(1/2 + it) is bounded by $\left( {\log t} \right)^{\frac{1}
{2} + o\left( 1 \right)}$\left( {\log t} \right)^{\frac{1}
{2} + o\left( 1 \right)}
, we show that for any given α > 0 the interval $(X,X + \sqrt X (\log X)^{{1 \mathord{\left/
{\vphantom {1 2}} \right.
\kern-\nulldelimiterspace} 2} + o\left( 1 \right)} ]$(X,X + \sqrt X (\log X)^{{1 \mathord{\left/
{\vphantom {1 2}} \right.
\kern-\nulldelimiterspace} 2} + o\left( 1 \right)} ]
contains an integer having no prime factor exceeding X
α
for all X sufficiently large. 相似文献
16.
M. Z. Garaev S. V. Konyagin Yu. V. Malykhin 《Proceedings of the Steklov Institute of Mathematics》2012,276(1):77-89
For fixed q ∈ (0, 4), prime p → ∞, and \(d \leqslant \exp \left( {c\sqrt {\ln p} } \right)\), where c > 0 is a constant, we obtain the asymptotics for the sum of qth powers of distances between neighboring residues of degree d modulo p. 相似文献
17.
18.
Danilo Bazzanella 《Archiv der Mathematik》2011,97(5):453-458
Let d(n) denote the number of positive divisors of the natural number n. The aim of this paper is to investigate the validity of the asymptotic formulafor \({x \to + \infty,}\) assuming a hypothetical estimate on the meanwhich is a weakened form of a conjecture of M. Jutila.
相似文献
$\begin{array}{lll}\sum \limits_{x < n \leq x+h(x)}d(n)\sim h(x)\log x\end{array}$
$\begin{array}{lll} \int \limits_X^{X+Y}(\Delta(x+h(x))-\Delta (x))^2\,{d}x, \end{array}$
19.
Graham Ellis 《Archiv der Mathematik》1996,66(6):467-469
20.
On square-full numbers in short intervals 总被引:1,自引:0,他引:1
Liu Honǵquan 《数学学报(英文版)》1990,6(2):148-164
It is shown that the number of square-full numbers in the interval
is asymptotically equal to
for every in the range 1/6>0.14254, which extends P.Shiu's range 1/6>0.1526. 相似文献