The Gaussian Law of Errors in the Theory of Additive Number Theoretic Functions
The Gaussian Law of Errors in the Theory of Additive Number Theoretic Functions
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DOI：
10.2307/2371483
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发表时间：
1940
影响因子：
1.7
通讯作者：
P. Erdös;M. Kac
中科院分区：
文献类型：
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作者：
P. Erdös;M. Kac
本文讨论统计方法在某些数论问题中的应用。Erdiis和Wintrier最近的研究？已经表明了数论中统计独立性概念的重要性;本文的目的是再次强调这一事实。这里可以提及的是，作为我们的主要定理的一个特殊情况，我们得到以下结果：如果v（m）表示~1的素因子的个数，En表示从1到12的那些整数的个数，其中V（W）< lg lg ~1 + WV 2 lg lg）1（W是任意的真实的数）：则
The present paper concerns itself with the applications of statistical methods to some number-theoretic problems. Recent inrestigations of Erdiis and Wintrier ? have shown the importance of the notion of statistical independence in number theory ; the purpose of this paper is to emphasize this fact once again. It may be mentioned here that we get as a particular case of our main theorem the following result : If v(m) denotes the number of prime divisors of ~1, and En the number of those integers from 1 up to 12 for which V(W) < lg lg ~1 + WV 2 lg lg )1 (W an arbitrary real number): then