共查询到20条相似文献,搜索用时 46 毫秒
1.
Let q?2 be an integer, χ be any non-principal character mod q, and H=H(q)?q. In this paper the authors prove some estimates for character sums of the form
2.
Yong Zhang Xiao-Yun Yang Zhi-Shan Dong 《Journal of Mathematical Analysis and Applications》2009,355(2):708-41
Let be a strictly stationary positively or negatively associated sequence of positive random variables with EX1=μ>0, and VarX1=σ2<∞. Denote , and γ=σ/μ the coefficient of variation. Under suitable conditions, we show that
3.
Dianliang Deng 《Journal of Mathematical Analysis and Applications》2011,376(1):136-153
Let X,X1,X2,… be a sequence of nondegenerate i.i.d. random variables with zero means. Set Sn=X1+?+Xn and . In the present paper we examine the precise asymptotic behavior for the general deviation probabilities of self-normalized sums, Sn/Wn. For positive functions g(x), ?(x), α(x) and κ(x), we obtain the precise asymptotics for the following deviation probabilities of self-normalized sums:
4.
H. Maier 《Journal of Number Theory》2009,129(7):1669-1677
Let f(x) be a real valued polynomial in x of degree k?4 with leading coefficient α. In this paper, we prove a non-trivial upper bound for the quantity
5.
6.
Tsz Ho Chan 《Journal of Number Theory》2008,128(5):1182-1194
We generalize Dirichlet's diophantine approximation theorem to approximating any real number α by a sum of two rational numbers with denominators 1?q1,q2?N. This turns out to be related to the congruence equation problem with 1?x,y?q1/2+?. 相似文献
7.
Let (|q|<1). For k∈N it is shown that there exist k rational numbers A(k,0),…,A(k,k−1) such that
8.
Yevhen Zelenyuk 《Journal of Combinatorial Theory, Series A》2008,115(2):331-339
Let G be an Abelian group and let be infinite. We construct a partition of A such that whenever (xn)n<ω is a one-to-one sequence in A, g∈G and m<ω, one has
(g+FSI((xn)n<ω))∩Am≠∅, 相似文献
9.
Zhi-Wei Sun 《Discrete Mathematics》2008,308(18):4231-4245
In this paper we study recurrences concerning the combinatorial sum and the alternate sum , where m>0, n?0 and r are integers. For example, we show that if n?m-1 then
10.
Michael Z. Spivey 《Discrete Mathematics》2007,307(24):3130-3146
We present a new approach to evaluating combinatorial sums by using finite differences. Let and be sequences with the property that Δbk=ak for k?0. Let , and let . We derive expressions for gn in terms of hn and for hn in terms of gn. We then extend our approach to handle binomial sums of the form , , and , as well as sums involving unsigned and signed Stirling numbers of the first kind, and . For each type of sum we illustrate our methods by deriving an expression for the power sum, with ak=km, and the harmonic number sum, with ak=Hk=1+1/2+?+1/k. Then we generalize our approach to a class of numbers satisfying a particular type of recurrence relation. This class includes the binomial coefficients and the unsigned Stirling numbers of the first kind. 相似文献
11.
Andrej Zlatoš 《Journal of Functional Analysis》2005,225(2):371-382
Let Ej be the eigenvalues outside [-2,2] of a Jacobi matrix with an-1∈?2 and bn→0, and μ′ the density of the a.c. part of the spectral measure for the vector δ1. We show that if bn∉?4, bn+1-bn∈?2, then
12.
Shaun Cooper 《Journal of Number Theory》2003,103(2):135-162
Let rk(n) denote the number of representations of an integer n as a sum of k squares. We prove that for odd primes p,
13.
Let 1 ? p ? ∞, 0 < q ? p, and A = (an,k)n,k?0 ? 0. Denote by Lp,q(A) the supremum of those L satisfying the following inequality:
14.
Let q>1 and m>0 be relatively prime integers. We find an explicit period νm(q) such that for any integers n>0 and r we have
15.
Let p(z) be a polynomial of degree n which does not vanish in |z|<k. It is known that for each q>0 and k?1,
16.
Ronald Evans 《Journal of Mathematical Analysis and Applications》2003,281(2):454-476
We consider the classical incomplete higher-order Gauss sums
17.
Let be a finite field and consider the polynomial ring . Let . A function , where G is a group, is called strongly Q-additive, if f(AQ+B)=f(A)+f(B) holds for all polynomials with degB<degQ. We estimate Weyl sums in restricted by Q-additive functions. In particular, for a certain character E we study sums of the form where is a polynomial with coefficients contained in the field of formal Laurent series over and the range of P is restricted by conditions on fi(P), where fi (1ir) are Qi-additive functions. Adopting an idea of Gel'fond such sums can be rewritten as sums of the form with . Sums of this shape are treated by applying the kth iterate of the Weyl–van der Corput inequality and studying higher correlations of the functions fi. With these Weyl sum estimates we show uniform distribution results. 相似文献
18.
Let , 1?μ?n, be a polynomial of degree n such that p(z)≠0 in |z|<k, k>0, then for 0<r?R?k, Dewan, Yadav and Pukhta [K.K. Dewan, R.S. Yadav, M.S. Pukhta, Inequalities for a polynomial and its derivative, Math. Inequal. Appl. 2 (2) (1999) 203-205] proved
19.
For a simplicial complex X and a field K, let .It is shown that if X,Y are complexes on the same vertex set, then for k?0
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