| 一类可加函数的均值估计 |
| |
| 引用本文： | 黄炜.一类可加函数的均值估计[J].西南民族学院学报(自然科学版),2014(4):578-581. |
| |
| 作者姓名： | 黄炜 |
| |
| 作者单位： | 宝鸡职业技术学院基础部,陕西宝鸡721013 |
| |
| 基金项目： | 国家自然科学基金项目（10671155）;陕西省自然科学基金项目（SJ08A28）资助. |
| |
| 摘 要： | 对任意正整数n,素因数和函数F(n)为F(1)=0,当n1且n的标准分解式为n=p1a1p2a2···prar时,F(n)=α1p1+α2·p2+···+αr·pr.设p(n)表示n的最小素因子.本文研究了可加函数(F(n)-p)2的值分布,并用初等方法得到了一个较强的渐近公式.
|
| 关 键 词： | 可加函数 最小素因子 均方值 渐近公式 |
An additive function and its mean value estimate |
| |
| HUANG Wei.An additive function and its mean value estimate[J].Journal of Southwest Nationalities College(Natural Science Edition),2014(4):578-581. |
| |
| Authors: | HUANG Wei |
| |
| Institution: | HUANG Wei ( Baoji Vocational and Technical College, Baoji 721013, P.R.C.) |
| |
| Abstract: | For any positive integer n, define F（1） = 0 And F（n） = a1p1 ＋a2·P2 ＋…＋ar·Pr ifn 〉 1, which satisfies n=P1^a1P2^an…Pr^ar which decomposes n into prime powers, let p（n） be the smallest prime divisor ofn. The main purpose of this paper is to use the elementary methods and the prime distribution to study the value distribution properties of （F（n） -p（n））2, and give one sharper asymptotic formula for it. |
| |
| Keywords: | additive function smallest prime divisor mean square value asymptotic formula |
| 本文献已被 CNKI 维普 等数据库收录！ |
