A divisor problem
A divisor problem
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DOI：
10.1007/bf03021203
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发表时间：
1930-12
期刊：
影响因子：
--
通讯作者：
E. C. Titchmarsh
中科院分区：
文献类型：
--
作者：
E. C. Titchmarsh
Adunanza del 24 marzo i929，x.设d（n）表示n的约数，设（i）Dp（x）-yd（p-l）其中p贯穿所有大于I的素数，l是常数整数。问题是确定Dp（x）在x~ oo时的行为。序列p-1的性质非常模糊;例如，不知道序列p-2是否包含无穷多个素数。所以一个关于p-i的问题，我们可以给出某种答案，是有一定意义的。其次，这是一个很好的练习，无论是在小学素数理论和理论的狄里希特的L-职能，并迫使我们协调大量的工作，这是目前相当分散。
Adunanza del 24 marzo i929, x. Let d (n) denote the number of divisors of n, and let (iI) Dp (x)--yd (p--l) where p runs through all prime numbers greater than I, and l is a constant integer. The problem is to determine the behaviour of Dp (x) as x~ oo. The properties of the sequence p--I are very obscure; for example, it is not known whether the sequence p--2 contains an infinity of primes or not. So a problem about p--I to which we can give some sort of answer has a certain interest. Secondly, it is an excellent exercise both in elementary prime-number theory and in the theory of DIRICHLET'S L-functions, and compels us to co ordinate a good deal of work which is at present rather scattered.