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Sur la répartition des valeurs des fonctions arithmétiques. Le nombre de facteurs premiers d'un entier
| Content Provider | Semantic Scholar |
|---|---|
| Author | Hwang, Hsien-Kuei |
| Copyright Year | 1998 |
| Abstract | Resume This paper is concerned with the quantity N ( x , m ), the number of positive integers n , 1⩽ n ⩽ x , for which Ω ( n )= m , where Ω: ( n ) denotes the total number of prime factors (counted with multiplicities) of n . The main purpose of this article is to present three powerful analytic methods, due, respectively, to Selberg, van der Waerden, and the author, the combination of which allows one to completely characterize the asymptotic behavior of the quantity N ( x , m ) as the second parameter varies through all its possible values, namely 1⩽ m ⩽(log x )/log 2. These methods constitute, in a certain sense, a compact and effective set of analytical tools and apply also to the distribution function associated with n ( x , m ). All these methods are quite general and applicable to many other arithmetic functions. |
| Starting Page | 135 |
| Ending Page | 152 |
| Page Count | 18 |
| File Format | PDF HTM / HTML |
| DOI | 10.1006/jnth.1997.2216 |
| Volume Number | 69 |
| Alternate Webpage(s) | http://algo.stat.sinica.edu.tw/hk/files/2005_07/pdf/On%20the%20distribution%20of%20the%20values%20of%20arithmetical%20functions.pdf |
| Alternate Webpage(s) | https://doi.org/10.1006/jnth.1997.2216 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
