孪生素数椭圆曲线E_的整数点

设p和q是孪生素数.本文讨论了椭圆曲线E_上的非平凡整数点.运用初等数论方法证明了该椭圆曲线至多有1组非平凡整数点(x,±y).     

On the Upper Bound of the Number of Primes in Arithmetic Progression

Let a and q be relatively prime positive integers and \pi(x,q,a) stand for the number of primes p\leq x congruent to a and q. H. Iwanice proved that \pi(x;q,q)<\frac{(2+\varepsilon)x}{\phi(q)log D} for any \varepsilon>0, x>x_0 (\varepsilon) and q\leq x^9/20-\varepsilon , where D=xq^-3/8. The author applies an improved estimation of the error term in the linear sieve, proves that for any \varepsilon>0, x>x_0 (\varepsilon) and q\leq x^5/11-\varepsilon , (1) is true.     

形如2kp+1的数的素性检验

本文初步探讨了如何快速检验一个大数n是素数(这里n-1含有大的素因子)的算法问题以及如何生成一个大素数p使得p-1有大的素因子q的算法问题.我们给出了形如n=2kp+1的数的素性检验的多项式时间算法,这里p是一个给定的大素数,k是正整数满足22k＜2kp.该算法的计算量为O(log32n).然后我们给出了生成一个大素数p使得p-1有大的素因子q的算法,其中q满足q＞(p-1)/log2(p-1).特别地,我们给出了判定并生成一个安全素数p的算法.     

表大偶數為一個不超過三個素數的乘積及一個不超過四個素數的乘積之和

<正> V.Brun最初在1920年證明了:每一充分大的偶數可表為兩個各不超過9個素數的乘積之和.簡記之為(9,9).後來,不少數學家改進與簡化了Brun方法,因此,Brun的結果也得到相應的改進,     

The exceptional set for the distribution of primes between consecutive powers

A well known conjecture about the distribution of primes asserts that between two consecutive squares there is always at least one prime number. The proof of this conjecture is quite out of reach at present, even under the assumption of the Riemann Hypothesis. This paper is concerned with the distribution of prime numbers between two consecutive powers of integers, as a natural generalization of the afore-mentioned conjecture.      

参数边界条件下奇型Sturm-Liouville算子的半逆问题

Sturm-Liouville算子的半逆问题讨论由一组谱和半区间上势函数唯一确定整个区间上势函数q(x).本文利用Koyunbakan和Panakhov的方法和[13]的结论,讨论(0,π)上的奇型Sturm-Liouville问题满足-y″+[q(x)-1/4sin2x]y=λy,参数边界条件y(0,λ)=0或y′(0,λ)-hy(0,λ)=0和y′(π,λ)+(aλ+b)y(π,λ)=0,证明一组谱和(π/2,π)上的势函数q(x)唯一确定(0,π)上的势函数q(x).     

On exponential sums over primes and application in Waring-Goldbach problem

In this paper, we prove the following estimate on exponential sums over primes: Let κ≥1,βκ=1/2 log κ/log2, x≥2 and α=a/q λsubject to (a, q) = 1, 1≤a≤q, and λ∈R. Then As an application, we prove that with at most O(N2/8 ε) exceptions, all positive integers up to N satisfying some necessary congruence conditions are the sum of three squares of primes. This result is as strong as what has previously been established under the generalized Riemann hypothesis.     

Terence Tao的一个问题

解决了Terence Tao提出的一个问题.证明了:设K≥2,N充分大,L_N为{-KN,…,KN}的任意子集,|L_N|=K.那么在[N,(1+1/K)N]中至少存在C_K N/(log N)个素数p,使得|kp+ja~i+l|为合数,其中1≤a,|j|,k≤K,1≤i≤K log N,l∈L_N,ja~i+l≠0,常数C_K0与K有关.     

ON IDEAL CLASS GROUPS AND UNITS IN TERMS OF THE QUADRATIC FORM x^2＋32y^2

§1. IntroductionIt is a classical topic to study, for quadratic number ?elds F = Q(√2p) with a prime p,the exact 2-power dividing the narrow class number h (F) and the norm of the fundamentalunit ε of F.The 2-primary subgroup of the narrow class group …     

一类两点边值问题的多重非负解

该文考虑两点边值问题[1/q(t)][q(t)y′(t)]′+p(t)f(y(t))= 0,λ_1 y(α)-λ_2y′(α)=0 and y(β)=B非负解的存在性, 其中p(t)可能在t=α或t=β附近具有奇异性, f(0)≥0, lim_(y→+∞)f(y)/y=+∞, 并且存在y>0, 使得f(y)<0.      

小区间上的素变数三角和估计

设A(n)为von Mangoldt函数且实数θ=95-83~(1/2)/121.当xθ+ε≤y≤x时,本文对于所有的α∈[0,1]给出了指数和S2(x,y;α)=∑x0,估计式∑x相似文献   

华林-哥德巴赫问题:两个平方,两个立方和两个四次方

令P_r表示素因子不超过r的殆素数,按重数计.作者证明了对于充分大的偶数N,方程N=x~2+p_1~2+p_2~3+p_3~3+p_4~4+p_5~4有解,其中x是殆素数P_6,p_j(j=1,…,5)是素数.     

关于形如（2^p＋1）／3的素数

设ｐ为奇素数,本文讨论（２＾ｐ＋１）／３的基本性质,并对ｐ〈６０００给出了素数和概率数。     

Lengths of the periods of the continued fraction expansion of quadratic irrationalities and on the class numbers of real quadratic fields

The fundamental result of the paper is the following theorem: suppose that the Riemann conjecture is valid for the Dedekind ζ-functions of all fields Then there exists a constant C>0 such that on the interval p≤x one can find at least Cx log⁻¹ x prime numbers p for which h(5p²)=2. Here h(d) is the number of proper equivalence classes of primitive binary quadratic forms of discriminant d. In addition, it is proved that . For these sequence of discriminants of a special form with increasing square-free part, one has obtained a nontrivial estimate from above for the number of classes. Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 160, pp. 72–81, 1987.     

特征标次数图是一种连通图的单群

对有限单群G,假设其不可约特征标次数图Δ(G)连通,且图顶点集ρ(G)=π_1∪π_2∪{p},其中|π_1|,|π_2|≥1,π_1∩π_2=θ,且π_1与π_2中顶点不相邻.证明了Δ(G)满足上面的假设的有限单群G只有4种:M_(11),J_1,PSL_3(4)或²B_2(q2B_2(q²),其中q2),其中q²一1是Mersenne素数.     

On the distribution of norms of prime ideals of a given class in arithmetic progressions

Let C be a class of ideals of the ring of algebraic numbers of an imaginary quadratic field. Let l and q be relatively prime integers, , and A₁ τ; 1. An asymptotic formula for the number π₁(x, q, l, C) of prime ideals belonging to the class C whose norms do not exceed x and lie in an arithmetic progression is obtained in this paper. Bibliography: 6 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 322, 2005, pp. 45–62.     

A remark on Fermat's last theorem

It is proved that the equation x^p + y^p + Z^p=Q, (xyz, p)=1 has no solutions in rational integers x, y, z for all odd prime numbers p for which q=pk + 1 is a prime number, k 82, k 0 (mod 3).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 67, pp. 223–224, 1977.     

论筛法及其有关的若干应用——殆素数的分布问题

<正> 本文的宗旨在于证明作者在[1]内所提及的全部结果,现在将本文的强果详述于下:定理1.命 F(x)表一无固定素因子的 k 次既约整值多项式.命(?)此处 w 是适合下面不等式的最小正整数(?)则在叙列{F(x)}中存在无限多个不超过 n 个素数的乘积.例如存在无限多个 x,使 x~3+2的素因子个数(包括相同的与相异的)不多于4.与此相类似,有定理2.设 k 为一正整数,命 n 适合(1)及(2),则当 x 充分大时,区间 x相似文献   

二阶微分系统奇异正定超线性周期边值问题的多重正解

主要研究了二阶微分系统具有奇异正定超线性周期边值问题多重正解的存在性问题,利用Leray-Schauder抉择定理和锥不动点定理给出了奇异正定超线性周期边值问题-(p(t)x′)′+q1(t)x=f1(t,x,y),t∈I=[0,1]-(p(t)y′)′+q2(t)y=f2(t,x,y)x(0)=x(1),x[1](0)=x[1](1)y(0)=y(1),y[1](0)=y[1](1)(1.1)的多重正解的存在性,其中非线性项fi(t,x,y)(i=1,2)在x=∞,y=∞点处超线性,在(x,y)=(0,0)处具有奇性.这里定义x[1](t)=p(t)x′(t),y[1](t)=p(t)y′(t)为准导数,其中系数p(t),qi(t)(i=1,2)是定义在[0,1]上的可测函数,且p(t)>0,qi(t)>0(i=1,2),a.e[0,1],fi(t,x,y)∈C(I×R×R,R+),R+=(0,+∞).     

关于特殊形式素数$p$的$\alpha p^2$ 模$1$的分布

证明了如果$0<\theta < \frac {2}{375}$, 则对于无理数$\alpha$, 存在无限个素数$p$, 使得$p+2$不超过4个素因子, 并满足不等式$\|\alpha p^2+\beta\|相似文献