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1.
Ajai Choudhry 《Journal of Number Theory》2005,110(2):403-412
This paper deals with the problem of finding n integers such that their pairwise sums are cubes. We obtain eight integers, expressed in parametric terms, such that all the six pairwise sums of four of these integers are cubes, 9 of the 10 pairwise sums of five of these integers are cubes, 12 pairwise sums of six of these integers are cubes, 15 pairwise sums of seven of these integers are cubes and 18 pairwise sums of all the eight integers are cubes. This leads to infinitely many examples of four positive integers such that all of their six pairwise sums are cubes. Further, for any arbitrary positive integer n, we obtain a set of 2(n+1) integers, in parametric terms, such that 5n+1 of the pairwise sums of these integers are cubes. With a choice of parameters, we can obtain examples with 5n+2 of the pairwise sums being cubes. 相似文献
2.
We study the approximation of the inverse wavelet transform using Riemannian sums. For a large class of wavelet functions, we show that the Riemannian sums converge to the original function as the sampling density tends to infinity. When the analysis and synthesis wavelets are the same, we also give some necessary conditions for the Riemannian sums to be convergent. 相似文献
3.
Dedekind和的一个性质 总被引:4,自引:0,他引:4
Dedekind和的Knopp等式是与Hecke算子有关的一个算术性质,本文不借助eta-函数的概念,给予Knopp等式的一个简短的初等证明,同时把Knopp等式拓广到广义Dedekind和中。 相似文献
4.
F. Chamizo 《Journal of Mathematical Analysis and Applications》2009,350(1):283-289
We combine exponential sums, character sums and Fourier coefficients of automorphic forms to improve the best known upper bound for the lattice error term associated to rational ellipsoids. 相似文献
5.
Shinji Fukuhara Noriko Yui 《Transactions of the American Mathematical Society》2004,356(10):4237-4254
We introduce an elliptic analogue of the Apostol sums, which we call elliptic Apostol sums. These sums are defined by means of certain elliptic functions with a complex parameter having positive imaginary part. When , these elliptic Apostol sums represent the well-known Apostol generalized Dedekind sums. Also these elliptic Apostol sums are modular forms in the variable . We obtain a reciprocity law for these sums, which gives rise to new relations between certain modular forms (of one variable).
6.
Stamatis Koumandos 《The Ramanujan Journal》2007,14(1):1-38
We establish a best possible extension of a famous Theorem of Vietoris about the positivity of a general class of cosine sums.
Our result refines and sharpens several earlier generalizations of this Theorem, and settles some open questions regarding
the possibility of further improvement of it. Some new inequalities for trigonometric sums are given. We show that our results
have applications within the context of positive sums of Gegenbauer polynomials and quadrature methods. We also obtain some
existing estimates for the location of zeros of certain trigonometric polynomials under a weakened condition on their coefficients.
2000 Mathematics Subject ClassificationPrimary—42A05; Secondary—42A32,26D05, 26D15, 33B15, 33C45
Dedicated to Richard Askey on the occasion of his 70th birthday 相似文献
7.
We study the approximation of the inverse wavelet transform using Riemannian sums.We show that when the Fourier transforms of wavelet functions satisfy some moderate decay condition,the Riemannian sums converge to the function to be reconstructed as the sampling density tends to infinity.We also study the convergence of the operators introduced by the Riemannian sums.Our result improves some known ones. 相似文献
8.
Régis Blache 《Mathematische Nachrichten》2007,280(15):1681-1697
In this paper we present a new method for evaluating exponential sums associated to a restricted power series in one variable modulo pl , a power of a prime. We show that for sufficiently large l, these sums can be expressed in terms of Gauss sums. Moreover, we study the associated L ‐functions; we show that they are rational, then we determine their degrees and the weights as Weil numbers of their reciprocal roots and poles. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
9.
Stavros Garoufalidis James E. Pommersheim 《Journal of the American Mathematical Society》2001,14(1):1-23
We study relations among special values of zeta functions, invariants of toric varieties, and generalized Dedekind sums. In particular, we use invariants arising in the Todd class of a toric variety to give a new explicit formula for the values of the zeta function of a real quadratic field at nonpositive integers. We also express these invariants in terms of the generalized Dedekind sums studied previously by several authors. The paper includes conceptual proofs of these relations and explicit computations of the various zeta values and Dedekind sums involved.
10.
In this paper, we use the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of Cochrane sums and general Kloosterman sums, and give two sharp asymptotic formulae. 相似文献
11.
David M. Mason 《Journal of Theoretical Probability》2006,19(4):911-930
We determine the cluster sets of certain self-normalized sums of i.i.d. random variables. In the process, we obtain a refined large deviation result for sums in the domain of attraction of a stable law. 相似文献
12.
WU Qun-ying 《高校应用数学学报(英文版)》2012,27(2):169-180
Consider a sequence of i.i.d. positive random variables. An universal result in almost sure limit theorem for products of sums of partial sums is established.We will show that the almost sure limit the... 相似文献
13.
P. E. Frenkel 《Proceedings of the American Mathematical Society》1998,126(11):3199-3200
We give a simple, elementary new proof of a generalization of the following conjecture of Paul Erdos: the sum of the elements of a finite integer set with distinct subset sums is less than 2.
14.
Arnold and Villaseñor (1999) raised several questions for upper records, including characterizing all limit distributions of normalized partial sums of upper records. We provide some answers in the case when the distribution from which the samples are drawn is bounded above. When the distribution is not bounded above, we give sufficient conditions on the distribution for the properly normalized partial sums to converge to a standard normal distribution. We show that our conditions are general enough so that the examples provided by Arnold and Villaseñor (1999) are covered by our results. 相似文献
15.
We compute covering numbers associated to the set of partial sums of orthogonal series by means of irrational rotations. The device is a new metric inequality linking the increment's norm of partial sums to the one of ergodic averages of rotations acting on a suitable L
2-element of the torus. This allows to compute the number of balls covering the whole set of partial sums, by means of rotations. 相似文献
16.
17.
Weighted trigonometric sums over a half-period 总被引:1,自引:0,他引:1
We derive formulas for evaluating weighted sums of trigonometric functions over evenly-spaced angles in the first quadrant. These results generalize those of a previous paper, where we considered trigonometric sums weighted by real, primitive, non-principal Dirichlet characters. 相似文献
18.
证明了 Burr分布和 Frechét分布的记录值序列的部分和是渐进对数正态的 ,从而解决了文[2 ]中的一个悬而未决的问题 相似文献
19.
本文利用Gauss和与原特征的性质以及DirichletL-函数的均值定理研究了超级Cochrane和与超级Kloosterman和的混合型均值,并给出了一个有趣的渐近公式. 相似文献