| Q_k(x)与F_k(x)的渐近公式 |
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| 引用本文： | 蔡迎春.Q_k(x)与F_k(x)的渐近公式[J].数学学报,1994,37(4):523-533. |
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| 作者姓名： | 蔡迎春 |
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| 作者单位： | 山东大学数学系!济南250100 |
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| 摘 要： | 设ｎ，ｋ为自然数，Ｇ（ｎ）阶群中的同构类数，Ｆｋ（ｘ）与Ｑｋ（ｘ）分别表示不超过ｘ的自然数中使Ｇ（ｎ）＝ｋ的自然数、无平方因子自然数的个数．本文的目的是用Ｂｒｕｎ筛法证明Ｑｋ（ｘ）的条件渐近公式并对Ｆｋ（ｘ）的渐近性质做出了推测．
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| 关 键 词： | Brun筛法 渐近公式 素数 群 同构类数 |
| 收稿时间： | 1991-12-16 |
| 修稿时间： | 1993-5-11 |
The Asymptotic Formulae for Q_k(x) and F_k(x) |
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| Cai Yengchun.The Asymptotic Formulae for Q_k(x) and F_k(x)[J].Acta Mathematica Sinica,1994,37(4):523-533. |
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| Authors: | Cai Yengchun |
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| Institution: | Cai Yengchun (Department of Mathematics, Shandong University, Ji'nan 250100, China) |
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| Abstract: | For natural number n and k, let G(n) denote the number of isomorphism classes of groups of order n, Fk(x) the number of n not exceeding x and G(n) = k, and Qk(x) the number of n hot exceeding x, square-free and G(n) = k. In this paper a conditional asymptotic formula is proved for Qk(x) and a conjecture is made for Fk(x) by Brun's sieve method. |
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| Keywords: | Brun's sieve method asymptotic formula prime group isomorphism classes |
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