On limiting distributions of arithmetic functions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866909388273352704 |
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| author | Das, Sourabhashis |
| author_facet | Das, Sourabhashis |
| contents | For a natural number n, let M(n) denote the maximum exponent of any prime power dividing n, and let m(n) denote the minimum exponent of any prime power dividing n. We study the second moments of these arithmetic functions and establish their limiting distributions. We introduce a new discrete probabilistic distribution dependent on a function f taking values in [0,1], study its first two moments, and provide examples of several arithmetic functions satisfying such distribution as their limiting behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08799 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On limiting distributions of arithmetic functions Das, Sourabhashis Number Theory Probability 11N37, 11K65 For a natural number n, let M(n) denote the maximum exponent of any prime power dividing n, and let m(n) denote the minimum exponent of any prime power dividing n. We study the second moments of these arithmetic functions and establish their limiting distributions. We introduce a new discrete probabilistic distribution dependent on a function f taking values in [0,1], study its first two moments, and provide examples of several arithmetic functions satisfying such distribution as their limiting behavior. |
| title | On limiting distributions of arithmetic functions |
| topic | Number Theory Probability 11N37, 11K65 |
| url | https://arxiv.org/abs/2411.08799 |