共查询到20条相似文献,搜索用时 6 毫秒
1.
Cemile Tosun 《Discrete Mathematics》2019,342(12):111618
In this paper, we derive explicit factorizations of generalized cyclotomic polynomials and generalized Dickson polynomials of the first kind of order , over finite field . 相似文献
2.
We present a new structure theorem for finite fields of odd order that relates multiplicative and additive properties in an interesting way. This theorem has several applications, including an improved understanding of Dickson and Chebyshev polynomials and some formulas with a number-theoretic flavor. This paper is an abridged version of two articles by the author. 相似文献
3.
Claus Fieker. 《Mathematics of Computation》2001,70(235):1293-1303
Based on an explicit representation of the Artin map for Kummer extensions, we present a method to compute arbitrary class fields. As in the proofs of the existence theorem, the problem is first reduced to the case where the field contains sufficiently many roots of unity. Using Kummer theory and an explicit version of the Artin reciprocity law we show how to compute class fields in this case. We conclude with several examples.
4.
We derive explicit factorizations of generalized cyclotomic polynomials of order and generalized Dickson polynomials of the first kind of order over finite field . 相似文献
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The relationship between the harmonicity and analyticity of a continuous map from the open unit disc to the underlying space
of a real algebra is investigated. 相似文献
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10.
Joachim König 《代数通讯》2018,46(6):2405-2416
11.
Factorization and symplectic uniton numbers for harmonic maps into symplectic groups 总被引:7,自引:0,他引:7
It is proved that any harmonic map ϕ : Ω →Sp(N) from a simply connected domain Ω ⊆R
2⋃ | ∞ | into the symplectic groupSp(N) ⊂U(2N) with finite uniton number can be factorized into a product of a finite number of symplectic unitons. Based on this factorization,
it is proved that the minimal symplectic uniton number of ϕ is not larger thanN, and the minimal uniton number of ϕ is not larger than 2N - 1. The latter has been shown in literature in a quite different way. 相似文献
12.
T. A. Springer 《Proceedings Mathematical Sciences》1994,104(1):207-216
The paper contains an exposition of the basic results on reduction theory in reductive groups over global fields, in the adelic
language. The treatment is uniform: number fields and function fields are on an equal footing.
Dedicated to the memory of Professor K G Ramanathan 相似文献
13.
G. Horváth 《Acta Mathematica Hungarica》2007,115(1-2):169-175
Let 0 ≦ a 1 < a 2 < ? be an infinite sequence of integers and let r 1(A, n) = |(i;j): a i + a j = n, i ≦ j|. We show that if d > 0 is an integer, then there does not exist n 0 such that d ≦ r 1 (A, n) ≦ d + [√2d + ½] for n > n 0. 相似文献
14.
Periodica Mathematica Hungarica - Let a1&;lt;... be an infinite sequence of positive integers, let k≥2 be a fixed integer and denote by Rk(n) the number of solutions of n=ai1+ai2+...+aik.... 相似文献
15.
Let q be a power of an odd prime. We prove that all -quadratic perfect nonlinear maps from to are equivalent. We also give a geometric method to find the corresponding equivalence explicitly. 相似文献
16.
Sándor Kiss 《Periodica Mathematica Hungarica》2005,51(2):31-35
Summary Let <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"7"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"8"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"9"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"10"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"11"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"12"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"13"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"14"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"15"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>\mathcal{A}=\{a_{1},a_{2},\dots{}\}$
$(a_{1} \le a_{2} \le \dots{})$ be an infinite sequence of nonnegative integers, and let $R(n)$ denote the number of solutions
of $a_{x}+a_{y}=n$ $(a_{x},a_{y}\in\mathcal{A})$. P. Erd?s, A. Sárk?zyand V. T. Sós proved that if $\lim_{N\to\infty}\frac{B(\mathcal{A},N)}{\sqrt{N}}=+\infty$
then $|\Delta_{1}(R(n))|$ cannot be bounded, where ${B(\mathcal{A},N)}$ denotes the number of blocks formed by consecutive
integers in $\mathcal{A}$ up to $N$ and $\Delta_{k}$ denotes the $k$-th difference. The aim of this paper is to extend this
result to $\Delta_{k}(R(n))$ for any fixed $k\ge2$. 相似文献
17.
L. Dewaghe. 《Mathematics of Computation》1998,67(223):1247-1252
Schoof's algorithm computes the number of points on an elliptic curve defined over a finite field . Schoof determines modulo small primes using the characteristic equation of the Frobenius of and polynomials of degree . With the works of Elkies and Atkin, we have just to compute, when is a ``good" prime, an eigenvalue of the Frobenius using polynomials of degree . In this article, we compute the complexity of Müller's algorithm, which is the best known method for determining one eigenvalue and we improve the final step in some cases. Finally, when is ``bad", we describe how to have polynomials of small degree and how to perform computations, in Schoof's algorithm, on -values only.
18.
Let K be an algebraic number field. We discuss the problem of counting the number of integral ideals below a given norm and obtain effective error estimates. The approach is elementary and follows a classical line of argument of Dedekind and Weber. The novelty here is that explicit error estimates can be obtained by fine tuning this classical argument without too much difficulty. The error estimate is sufficiently strong to give the analytic continuation of the Dedekind zeta function to the left of the line R(s)=1 as well as explicit bounds for the residue of the zeta function at s=1. 相似文献
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Xuejun Guo 《代数通讯》2013,41(9):2889-2893