Moyennes effectives de fonctions multiplicatives complexes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2017
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| _version_ | 1866916854281273344 |
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| author | Tenenbaum, Gérald |
| author_facet | Tenenbaum, Gérald |
| contents | We establish effective mean-value estimates for a wide class of multiplicative arithmetic functions, thereby providing (essentially optimal) quantitative versions of Wirsing's classical estimates and extending those of Halász. Several applications are derived, including: estimates for the difference of mean-values of so-called pretentious functions, local laws for the distribution of prime factors in an arbitrary set, and weighted distribution of additive functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1709_01315 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Moyennes effectives de fonctions multiplicatives complexes Tenenbaum, Gérald Number Theory 11N56, 11K65, 11N37, 11N60, 11N64 We establish effective mean-value estimates for a wide class of multiplicative arithmetic functions, thereby providing (essentially optimal) quantitative versions of Wirsing's classical estimates and extending those of Halász. Several applications are derived, including: estimates for the difference of mean-values of so-called pretentious functions, local laws for the distribution of prime factors in an arbitrary set, and weighted distribution of additive functions. |
| title | Moyennes effectives de fonctions multiplicatives complexes |
| topic | Number Theory 11N56, 11K65, 11N37, 11N60, 11N64 |
| url | https://arxiv.org/abs/1709.01315 |