Un crible minorant effectif pour les entiers friables
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909870214610944 |
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| author | Mounier, Adrien |
| author_facet | Mounier, Adrien |
| contents | Let $\mathcal{A}$ be a finite set of positive integers and $y\geq 1$. We give an effective lower bound of the cardinality of the set $\{n\in\mathcal{A};\,p|n\Longrightarrow p\leq y\}$ under the condition of a good knowledge of the level of distribution of the set $\mathcal{A}$. Some consequences are studied: an application to the friable values of irreducible polynomials or binary forms with integer coefficients, and an application to shifted friable numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13198 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Un crible minorant effectif pour les entiers friables Mounier, Adrien Number Theory 11N25, 11N32, 11N35 Let $\mathcal{A}$ be a finite set of positive integers and $y\geq 1$. We give an effective lower bound of the cardinality of the set $\{n\in\mathcal{A};\,p|n\Longrightarrow p\leq y\}$ under the condition of a good knowledge of the level of distribution of the set $\mathcal{A}$. Some consequences are studied: an application to the friable values of irreducible polynomials or binary forms with integer coefficients, and an application to shifted friable numbers. |
| title | Un crible minorant effectif pour les entiers friables |
| topic | Number Theory 11N25, 11N32, 11N35 |
| url | https://arxiv.org/abs/2402.13198 |