共查询到20条相似文献,搜索用时 375 毫秒
1.
设Fq表示有q个元素的有限域,q为素数的方幂,f(x)=xn+a1xn-1+…+an-1x+an∈Fq[x].当n≥7时,文[8]指出存在Fq上可预先指定a1,a2的n次本原多项式.本文讨论了剩余的n=5,6两种情形,利用有限域上的两类特征和估计及Cohen筛法(见[4,6]),改进了文[8]中关于本原解个数的下界,并得到当n=5,6时,在特征为奇的有限域上存在可预先指定前两项系数的n次本原多项式. 相似文献
2.
3.
令Fq是具有q个元素的有限域,这里q是一个奇素数的幂,给出了Fq的加法群中的一些差集,并计算了它们的参数. 相似文献
4.
设有限域Fq,文献[1]构造性的证明了结论:Map(Fnq,Fq)中的每个元素都可以唯一的表示成Fq[x1,…,xn]中次数不超过q-1的多项式.本文利用Groebner基与多项式映射的相关结论,首先给出了该结论一个更为简明的证明,并进一步得到有限域上代数簇的多项式映射之间一个更为一般的性质. 相似文献
5.
设l为一奇正整数,q是某素数的方幂,二者满足l|q-1,记s=(q-1)/l;又设Fq是一个q元有限域,r,e为正整数,(e,l)=1.本文应用序列{an=∑(l-1)/2t=1(2(-1)t-1cos(tπ/l))n}∞n=-∞的性质给出了当l=9时Fq上的二项式f(x)=xr(1+xes)成为Fq上的置换多项式的充要条件. 相似文献
6.
设 Fq是特征为 2的有限域 ,本文研究了 Fq上 2 ν+δ+t级奇异伪辛群 Ps2ν+δ+ t(Fq) (δ=1或 2 )的 Carter子群的存在性及结构 .得到的结果为 :若 q>2 ,Ps2ν+δ+ t(Fq)中不含 Carter子群 ,若 q=2 ,Ps2ν+δ+ t(Fq)的 Carter子群为它的 Sylow2 -子群的正规化子 . 相似文献
7.
特征不为 2 的有限域上酉群的极小生成元集 总被引:7,自引:0,他引:7
设K=Fq2为含有q2个元素的有限域,q为奇素数的幂,*:a→a*=aq是Fq2的一个二阶自同构.本文用几何方法证明了除K为F32而n=4的情形外,Fq2上的酉群Un(V)可由2个元素生成. 相似文献
8.
确定有限域上给定周期的不可约多项式的个数以及利用低次不可约多项式构造高次不可约多项式 总被引:5,自引:0,他引:5
主要利用较献[4]更为简明的方法证明了有关有限域Fq(q为一个素数幂)上的以l为周期的n次不可约多项式的个数的结论。另外,本结合结合初等数论知识得到了前面这个结论的几个推论,并对利用低次不可约多项式构造高次不可约多项式进行了研究。 相似文献
9.
设Fq(T)=k, p是Fq的特征, l是奇素数, (Z/lZ)*= q ,M=Dl+d,d=ld0, Fq*, d0,D是Fq[T]中首一多项式, D 1,d0|Dl-1, M是l-幂自由的,记=(lM-D)l d,K为K=k(lM)的基本单位, K<0, 我们有结果: =Kpilj, j 0,1, 0 i e, 其中e是l的p-adic表示中p的最高幂次数. 相似文献
10.
11.
In this article, we study the bivariate Fibonacci and Lucas p-polynomials (p ? 0 is integer) from which, specifying x, y and p, bivariate Fibonacci and Lucas polynomials, bivariate Pell and Pell-Lucas polynomials, Jacobsthal and Jacobsthal-Lucas polynomials, Fibonacci and Lucas p-polynomials, Fibonacci and Lucas p-numbers, Pell and Pell-Lucas p-numbers and Chebyshev polynomials of the first and second kind, are obtained. Afterwards, we obtain some properties of the bivariate Fibonacci and Lucas p-polynomials. 相似文献
12.
13.
We give an analog of exceptional polynomials in the matrix-valued setting by considering suitable factorizations of a given second-order differential operator and performing Darboux transformations. Orthogonality and density of the exceptional sequence are discussed in detail. We give an example of matrix-valued exceptional Laguerre polynomials of arbitrary size. 相似文献
14.
Roman Witu?a 《Journal of Mathematical Analysis and Applications》2006,324(1):321-343
In this paper some new properties and applications of modified Chebyshev polynomials and Morgan-Voyce polynomials will be presented. The aim of the paper is to complete the knowledge about all of these types of polynomials. 相似文献
15.
We exploit difference equations to establish sharp inequalities on the extreme zeros of the classical discrete orthogonal polynomials, Charlier, Krawtchouk, Meixner and Hahn. We also provide lower bounds on the minimal distance between their consecutive zeros. 相似文献
16.
Frank Filbir Roland Girgensohn Anu Saxena Ajit Iqbal Singh Ryszard Szwarc 《Journal of Computational Analysis and Applications》2000,2(2):177-213
For an orthogonal polynomial system
and a sequence
of nonzero numbers,let
be the linear operator defined on the linear spaceof all polynomials via
for all
.We investigate conditions on
and
under which
can simultaneously preserve the orthogonality ofdifferent polynomial systems. As an application, we get that for
, a generalized Laguerre polynomial system, no
can simultaneously preserve the orthogonality of twoadditional Laguerre systems,
and
, where
and
. On the other hand, for
,the Chebyshev polynomial system and
,
simultaneously preserves the orthogonality of uncountablymany kernel polynomial systems associated with p. We study manyother examples of this type. 相似文献
17.
We characterize the class of ultraspherical polynomials in between all symmetric orthogonal polynomials on via the special form of the representation of the derivatives by
18.
Permutation polynomials of the form 总被引:1,自引:1,他引:0
Jin Yuan Cunsheng Ding Huaxiong Wang Josef Pieprzyk 《Finite Fields and Their Applications》2008,14(2):482-493
Recently, several classes of permutation polynomials of the form (x2+x+δ)s+x over have been discovered. They are related to Kloosterman sums. In this paper, the permutation behavior of polynomials of the form (xp−x+δ)s+L(x) over is investigated, where L(x) is a linearized polynomial with coefficients in . Six classes of permutation polynomials on are derived. Three classes of permutation polynomials over are also presented. 相似文献
19.
The sequence of orthogonal polynomials
is said to be classical if
is also orthogonal. The aim of this paper is to find the sequences
which have the property that
is also orthogonal. We prove that sequences, with this property have to be, classical and belong either to the set of Laguerre or Jacobi polynomials, where in the Laguerre case c has to be zero and in the Jacobi case c = ±1. 相似文献
20.
V. V. Karachik 《Proceedings of the American Mathematical Society》2004,132(4):1049-1058
New special functions called -functions are introduced. Connections of -functions with the known Legendre, Chebyshev and Gegenbauer polynomials are given. For -functions the Rodrigues formula is obtained. 相似文献