数论函数 $\Omega_k$ 的动力系统

本文推广了Goldring$^{[1]}$关于一个数论函数的动力系统的相关结果.     

关于不同因子分解的数目

设f(n)表示分解自然数n(>1)为大于1的整数因子乘积的所有方式的数目(不计因子的顺序),并设0<β<1,N(x,β)=Card{n≤x,f(n)≥n~β}.本文分别估计了N(x,β)和f(n))的值.     

Primes in progressions to moduli with a large power factor

On average, primes are uniformly distributed in short arithmetic progressions whose moduli may be divisible by high-powers of a given integer. In celebration of the seventieth birthday of Richard Askey. 2000 Mathematics Subject Classification Primary—11N13     

对含有整数最小素因子的倒数的某些和的估计

设p(n)表示整数n>1的最小素因子.本文得到了(?),v≥0的渐近式,此处f_v(n)是一类数论函数.     

与素数生成之筛法有关的周期性（英文）

考虑与埃拉托色尼(Eratosthenes)筛法稍有不同的一种筛法以生成素数.我们获得某种模式的周期性与镜像对称性.     

一个素变数丢番图不等式

本文证明了如果1相似文献   

Reductions of Tensor Categories Modulo Primes

We study good (i.e., semisimple) reductions of semisimple rigid tensor categories modulo primes. A prime p is called good for a semisimple rigid tensor category 𝒞 if such a reduction exists (otherwise, it is called bad). It is clear that a good prime must be relatively prime to the Müger squared norm |V|² of any simple object V of 𝒞. We show, using the Ito–Michler theorem in finite group theory, that for group-theoretical fusion categories, the converse is true. While the converse is false for general fusion categories, we obtain results about good and bad primes for many known fusion categories (e.g., for Verlinde categories). We also state some questions and conjectures regarding good and bad primes.     

Asymptotic Periodicity of Primes Associated to Multigraded Modules

In this paper, we investigate the asymptotic behavior of the set of primes associated to a graded ring extension of Noetherian multigraded rings and modules, and prove that the periodicity occurs in a cone. We also prove the same asymptotic behavior of the grade. The previous known results on this subject are recovered as a special case.     

Function Decompositions Related to the Luzin N-property

We introduce a class of continuous completely regular functions satisfying the N-property. We obtain a decomposition of an arbitrary continuous function into the sum of two functions the first of which is completely regular and the second does not enjoy the N-property. We define a class of strongly regular Borel functions for which we prove the Luzin N-property. We demonstrate that the image of every Lebesgue measurable set of a strongly regular function is measurable. From an arbitrary Borel function we extract a strongly regular function and a function that does not enjoy the N-property.     

素变数线性三角和的估计

设实效满足（ａ，ｑ）＝１：｜θ｜≤１．Ｎ≥３是一个整数。记ｒ＝ｌｏｇＮ，ｅ（ａｎ）＝ｅ￣（２πｉａｎ），为Ｍａｎｇｏｌｄｔ函数。在本文中，我们证明了     

关于双随机循环矩阵中的素元(英文)

非负矩阵中的素元分类问题在控制和系统论中有重要的应用.本文将研究由G.Picci等所提出的关于双随机循环矩阵中素元的一个问题和一个猜想,得到了一个判别具有位数5的n阶双随机循环矩阵不是素元的充要条件,给出了猜想成立的一些充分条件.     

Smarandache函数的几类相关方程的解

设φ(n),S(n)分别表示正整数n的Euler函数和Smarandache函数,利用初等的方法和技巧,依据Smarandache函数计算公式,给出k的方程φ(p~αm)=S(p~(ακ))的所有解,其中p为素数,α,m为正整数且gcd(m,p)=1,由此得到方程φ(n)=S(n~k)的所有解(n,k)进而确定了满足条件S(n)|σ(n)的全部正整数n.最后,根据莫比乌斯变换反演定理证明了方程φ(n)=∑_(d|n)S(d)仅有两个解,分别为n=2~5和n=3×2~5.     

涉及分担集的整函数的唯一性

In this paper,uniqueness of entire function related to shared set is studied.Let f be a non-constant entire function and k be a positive integer,d be a finite complex number.There exists a set S with 3 elements such that if f and its derivative f（k）satisfy E（S,f）= E（S,f（k））,and the zeros of f（z）-d are of multiplicity ≥ k ＋ 1,then f = f（k）.     

Products of Ratios of Consecutive Integers

Take the product of the numbers (n/(n+1))^∊_n for 1≤ n < N, where each ∊_n is ± 1. Express the product as a/b in lowest terms. Evidently the minimal possible value for a over all choices for ∊_n is 1; just take each ∊_n = 1, or each ∊_n = 0. Denote the maximal possible value of a by A(N). It is known from work of Nicolas and Langevin that (log 4+o(1))N≤ log A(N)≤(2/3+o(1))Nlog N. Using the Rosse–Iwaniec sieve, we improve the lower bound to the same order of magnitude as the upper bound.For Jean-Louis Nicolas, on his sixtieth birthday2000 Mathematics Subject Classification: Primary—11N56; Secondary—11N36     

稀疏素数集中的Waring-Goldbach问题

本文研究了Ｗａｒｉｎｇ Ｇｏｌｄｂａｃｈ问题（ｋ＝２）与Ｐｉａｔｅｔｓｋｉ Ｓｈａｐｉｒｏ素数定理的混合问题，从而进一步深化了华罗庚教授的经典结果     

关于一个新数论函数的混合均值

Let p and q be two distinct primes,epq(n) denotes the largest exponent of power pq which divides n.In this paper,we study the mean value properties of function epq(n), and give some hybrid mean value formulas for epq(n) and Dirichlet divisor function d(n).     

关于Genocchi数和Riemann Zeta-函数的一些恒等式

利用计算技巧给出了由Ｇｅｎｏｃｃｉ数和Ｒｉｃｍａｎｎ Ｚｅｔａ－函数组成的和式的递归关系，得到了一些关于Ｇｅｎｏｃｃｈｉ Ｚｅｔａ－函数的恒等式。     

关于Genocchi数和Riemann Zeta-函数的一些恒等式

利用计算技巧给出了由Ｇｅｎｏｃｃｉ数和ＲｉｅｍａｎｎＺｅｔａ－函数组成的和式的递归关系，得到了一些关于Ｇｅｎｏｃｃｈｉ数和ＲｉｅｍａｎｎＺｅｔａ－函数的恒等式     

Interpolation for Function Spaces Related to Mixed Boundary Value Problems

Interpolation theorems are proved for Sobolev spaces of functions on nonsmooth domains with vanishing trace on a part of the boundary.