On the Sums of three or more primes in arithmetic progressions;
关于算术数列中三个或多个素数的和
Diophantine approximation by prime varibles in arithmetic progressions;
算术数列中的素变数丢番图逼近
On the integer represented as the product of k prime numbers in arithmetic progression;
关于表整数为算术数列中k个素数的乘积
We extend Goldbach-Vinogradov s Theorem into arithmetic progressions, our result is as follows.
本文考虑Goldbach-Vinogradov定理在算术数列中的推广,我们的结果是:设k1,k2,k3是任意正整数,ι1,ι2,ι3是整数,满足(ι_j,k_j)=1,1≤j≤3,再设N是充分大的奇数,满足N≡ι1+ι2+ι3(mod(k1,k2,k3)),(ι_i+ι_j-N,k_i,k_j)=1,1≤i<j≤3,则存在一个实效常数0<δ<1,使得当K≤N~δ时,方程 N=p1+p2+p3,pj≡ι_j(mod k_j),j=1,2,3有素数解p1,p2,p3,其中K=max{2,k1,k2,k3}。
The principal purpose of this paper is to consider the bounds of solutions of the cubic equationwith the prime variables in arithmetic progressions modulo k > 1.
本文的主要目的是估计三次素变数方程的解在模k≥1算术数列中的上界。
Sums of three or more primes in arithmetical progressions;
算术数列中三个或多个素数的和
The distribution of weakly composite numbers into arithmetical progression is considered ,and (two) asymptotic formulas are obtained.
把弱合数的分布推广到算术数列中 ,给出了两个渐近公
This paper gives a construction of the set of arithmetic numbers and proves some qualities of the set of arithmetic numbers.
给出算术数集的一种构造，并证明算术数集的有关性质。