1) arithmetical number
算术数
2) arithmetic progression
算术数列
1.
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
2.
Diophantine approximation by prime varibles in arithmetic progressions;
算术数列中的素变数丢番图逼近
3.
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
3) arithmetical function
算术函数
1.
Two new arithmetical functions and their mean values;
两个新的算术函数及其均值
2.
A new arithmetical function and its mean value;
一个新的算术函数及其均值
3.
Mean value problems of arithmetical functions play an important role in the study of analytic number theory,and they relate to many famous number theoretic problems.
引入了两个新的算术函数,并利用Perron公式给出了两个均值公式。
4) arithmetic progression
算术级数
1.
They also remarked that Heath-Brown gave explicitly infinitely many 4-term arithmetic progressions,where each term can be written as sums of two squares.
Heath-Brown具体构造出无穷多组4项算术级数,其中每项均能表示为两个正整数的平方和。
2.
It has been proved that the primes contain arbitrarily long arithmetic progressions.
已有结论表明:素数集中存在任意长的算术级数。
3.
In this article, we prove that the ternary Goladbach problem in arithmetic progression can be solved for almost all large positive moduli, where the moduli can be as large as AT1/6-ε.
本文考察了几乎所有模的算术级数中的奇数Goldbach问题。
5) Arithmetica Integra
《整数算术》
6) arithmetic progressions
算术数列
1.
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}。
2.
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。
补充资料：R阶差数列
相邻两项相减,得到一个新数列,一直如此操作直到得到常数列,减了几次,就称为几阶差数列
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条