共查询到20条相似文献,搜索用时 0 毫秒
1.
We consider some new alternating double binomial sums. By using the Lagrange inversion formula, we obtain explicit expressions of the desired results which are related to a third-order linear recursive sequence. Furthermore, their recursive relation and generating functions are obtained. 相似文献
2.
利用广义高阶Bernoulli数的性质及Dirichlet L-函数的均值定理,研究了Gauss和及广义Kloosterman和与广义高阶Bernoulli数的均值性质,并给出两个有趣的渐近公式. 相似文献
3.
In this paper,we give several identities of finite sums and some infinite series involving powers and inverse of binomial coefficients,which extends the results of T.Trif. 相似文献
4.
In this paper, generalizing the result in [9], I construct strongly regular Cayley graphs by using union of cyclotomic classes of and Gauss sums of index w, where is even. In particular, we obtain three infinite families of strongly regular graphs with new parameters. 相似文献
5.
《数学研究通讯:英文版》2017,(4):359-362
In this article,we analyze the lower bound of the divisibility of families of exponential sums for binomials over prime field.An upper bound is given for the lower bound,and,it is related to permutation polynomials. 相似文献
6.
给出指数2情形下阶数为2l_1~(r1)l_1~(r2)的高斯和的显式计算公式.证明方法直接利用Stickelberger理想分解定理,进而结果独立于其他指数2情形高斯和的结果而成立. 相似文献
7.
Matthew Fickus 《Journal of Fourier Analysis and Applications》2009,15(3):413-427
In a finite-dimensional complex Euclidean space, a maximally equiangular frame is a tight frame which has a number of elements
equal to the square of the dimension of the space, and in which the inner products of distinct elements are of constant magnitude.
Though the general question of their existence remains open, many examples of maximally equiangular frames have been constructed
as finite Gabor systems. These constructions involve number theory, specifically Schaar’s identity, which provides a reciprocity
formula for quadratic Gauss sums. To be precise, Zauner used Schaar’s identity to compute the spectrum of a chirp-Fourier
operator, the eigenvectors of which he conjectured to be well-suited for the construction of maximally equiangular Gabor frames.
We provide two new characterizations of such frames, both of which further confirm the relevance of the theory of Gauss sums
to this area of frame theory. We also show how the unique time-frequency properties of a particular cyclic chirp function
may be exploited to provide a new, short and elementary proof of Schaar’s identity.
相似文献
8.
9.
Gauss和与广义Kloosterman和的几个新的恒等式 总被引:5,自引:1,他引:4
主要应用Gauss和的性质和解析方法来研究Gauss和与广义Kloosterman和之间的关系,并且给出了几个有趣的恒等式. 相似文献
10.
Some extremal problems for the sums of binomial coefficients that arise in research on estimating the computational complexity of discrete optimization algorithms are examined. These extremal problems are solved using the theory of majorization and useful inequalities are introduced for the sums of binomial coefficients. 相似文献
11.
设$a$, $b$和$n$为正整数,且$a>b$,我们证明了下面的整除性质: 对所有正整数$n$, 我们有$$(2bn+1)(2bn+3)(2bn+5){2bn\choose bn}\Big|15(a-b)(3a-b)(5a-b)(5a-3b){2an \choose an}{an\choose bn},$$ 上述整除式推广了杨全会一文中的相关结论.且对所有正整数$n$,我们证明了下面的整除性质:$$(6n+1){4n\choose n}\Big|{12n\choose 6n}{2n\choose n},\ (12n+1){5n\choose n}\Big|{15n\choose 3n}{3n-1\choose n-1},$$ $$(18n+1){12n\choose 9n}{8n\choose 2n}\Big| {24n\choose 18n}{4n\choose 2n}{6n\choose 3n}.$$更多类似的整除性质可以给出. 相似文献
12.
三次高斯和与Kloosterman和的线性递推公式 总被引:1,自引:1,他引:1
应用三角和方法以及高斯和的若干性质,研究三次高斯和与Kloosterman和的一类高次混合均值的计算问题,本文给出该混合均值的一个有趣的线性递推公式.同时,还应用该递推公式,得到三次高斯和与Kloosterman和的高次混合均值的一系列较强的渐近公式. 相似文献
13.
In this note, we give a construction of strongly regular Cayley graphs. The presented construction is based on choosing cyclotomic classes in finite fields, and our results generalize ten of the eleven sporadic examples of cyclotomic strongly regular graphs given by Schmidt and White [B. Schmidt, C. White, All two-weight irreducible cyclic codes, Finite Fields Appl. 8 (2002), 321–367] into infinite families. These infinite families of strongly regular graphs have new parameters. The main tools that we employed are relative Gauss sums instead of explicit evaluations of Gauss sums. 相似文献
14.
我们用三角和的性质研究一类三次Gauss和与两项指数和混合均值的计算问题,并给出一个精确的计算公式. 相似文献
15.
16.
17.
18.
The main purpose of this paper is using residue system and character sums methods to investigate the mean value properties of general k-th Gauss sums,and two exact calculating formulas are given. 相似文献
19.
利用已知级数,通过裂项构造出一批新的二项式系数倒数级数,它们的分母分别含有1到4个奇因子与二项式系数的乘积表达式.所给出二项式系数倒数级数的和式是封闭形的. 相似文献
20.