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1.
The author shows that K2Z[1+(-35的平根号)/2 ]?A ≈Z/2Z. The method of proof is a generalization of the Tate‘s method.  相似文献   

2.
Consider the sequence of algebraic integers un given by the starting values u0=0,u1=1 and the recurrence u_(n+1)=(4cos~2(2π/7)-1)u_n-u_(n-1).We prove that for any n ■{1,2,3,5,8,12,18,28,30}the n-th term of the sequence has a primitive divisor in Z[2 cos(2π/7)].As a consequence we deduce that for any sufficiently large n there exists a prime power q such that the groupcan be generated by a pair x,y with χ~2=y~3=(xy)~7=1 and the order of the commutator[x,y]is exactly n.The latter result answers in affirmative a question of Holt and Plesken.  相似文献   

3.
设n为正整数,利用不定方程x~2+13y~2=n存在整数解的充要条件,证明了整环Z[(-13)~(1/2)]中不可约元的结构定理.  相似文献   

4.
Let Z, N, Q be the sets of all integers, positive integers and rational numbers, respectively.Let D1, D2 be distinct positive integers, and let . The simultaneous Pell equationsarise in connection with a variety of classical problems on number theory and arithmetic algebraicgeometry. As has been noted by K. One[1], the solutions (x, y, z) of (1) imply the existence ofrational points of infinite order on the elliptic curveLet p, q be twin primes withRecently, Qiu Derong and Zhang Xianke[2…  相似文献   

5.
In this paper we discuss the convergence of a modified Newton's method presented by A. Ostrowski [1] and J.F. Traub [2], which has quadratic convergence order but reduces one evaluation of the derivative at every two steps compared with Newton's method. A convergence theorem is established by using a weak condition a≤3-2(2~(1/2)) and a sharp error estimate is given about the iterative sequence.  相似文献   

6.
Let △_(m,n)~(2)be a subdivision of D:[a,b]×[c,d](Fig.1),_1arelengths of[a,b]and[c,d]respectively,and h_1=_1/m,h_2=_2/n.  相似文献   

7.
[1] proved that S_n(x) was uniquely determined, and gave the error bounds of approximation of f(x) ∈C~4 [0,1] by S_n(x). B. K. Swartz and R. S. Varga [2] also gave the degree of approximation of f(x) ∈C~6 [0, 1] by S_n(x). Z. R. Guo [3] obtained the saturation theorem for this approximation. Z. R. Guo [4-5] were also concerned in this kind of interpolation and gave the degree of approximation. In this paper we consider the general lacunary interpolation by quintic splines.  相似文献   

8.
In this paper,the automorphism group of G is determined,where G is a 4 × 4 upper unitriangular matrix group over Z.Let K be the subgroup of AutG consisting of all elements of AutG which act trivially on G/G,G /ζG and ζG,then (i) InnG ■ K ■ AutG;(ii) AutG/K≌=G1×D8×Z2,where G1=(a,b,c|a4=b2=c2=1,ab=a-1,[a,c]= [b,c]=1 ;(iii) K/Inn G≌=Z×Z×Z.  相似文献   

9.
Let Z be a topological space and mapping A2 :Z→B(H) with closed range R(A2 ) be continuous . Some necessary and sufficient conditions of the continuity of M-P inverses A z+ are given in [1], [2]. It is one of them that AZ+ is continuous if ana only if AZ+ is locallybounded. In this paper, we discuss the following problem: if limA n = A0 in B(H) and ||An+||is unbounded (i.e. the above necessary and sufficient condition fails), what h in H will make the equations: limAm+ h = A0+ h or w-limAn+ h= A 0+ h be true. For this purpose three theorems and an error estimation are given in this paper.  相似文献   

10.
林群 《数学学报》1987,30(2):216-219
<正> 1972年A.Weitsman[1]证明对于下级有限的亚纯函数f(Z),有∑δ~(1/3)(a,f)<+∞,其中a是复数.本文在f(Z)是整函数的情况下,把这一结果推广到亏函数. 定理 设f(Z)是下级μ有限的整函数,则∑δ~(1/3)(a(Z),f)<+∞,其中a(Z)是满足T(r,a(Z))=o{T(r,f)}的亚纯函数.  相似文献   

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