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单词 Arithmetic function
释义

Arithmetic function

英语例句库

Realizing arithmetic function of sunlight analysis, and giving out some simulation and experimentative results.

给出了实验与模拟分析结果。

中文百科

算术函数

在数论上,算术函数(或称数论函数)指定义域为正整数、陪域为复数的函数,即f: \mathbb{Z}^{+} \rightarrow\mathbb{C}。每个算术函数都可视为复数的串行。

最重要的算术函数是积性及加性函数。算术函数的最重要操作为狄利克雷卷积,对于算术函数集,以它为乘法,一般函数加法为加法,可以得到一个阿贝尔环。

而且,由于f*g=0能够推出f=0或g=0,所以这一交换环是整环(Integral Domain),详见GTM164的附录。

(通常不称交换环为阿贝尔环,这一叫法只在群的情形下被普遍使用)

英语百科

Arithmetic function 算术函数

The chaotic course of Ω(n) through the natural numbers ( A001222): Beginning on the height of the red line the two least significant binary digits of Ω(n) of all positive odd n below 1200 are represented by a line up (digit 1) or a line down (digit 0). The additional replacement of the “↗↘” of the semiprimes without prime factors below 5 by only one line down (here blue) even almost brings a balance between the ups and downs. The prime numbers are marked orange: orange lines for the Gaussian primes and for the other primes p additional the number x in orange so that p = x2 + y2 = (x + yi) (x – yi) = –i (x + yi) (y + xi) and x < y for natural x and y ( A002331).

In number theory, an arithmetic, arithmetical, or number-theoretic function is a real or complex valued function f(n) defined on the set of natural numbers (i.e., positive integers) that "expresses some arithmetical property of n".

An example of an arithmetic function is the divisor function whose value at a positive integer n is equal to the number of divisors of n.

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更新时间:2025/6/20 4:24:52