An extension of smooth numbers: multiple dense divisibility
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909805281542144 |
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| author | Sarajian, Garo Weingartner, Andreas |
| author_facet | Sarajian, Garo Weingartner, Andreas |
| contents | The $i$-tuply $y$-densely divisible numbers were introduced by a Polymath project, as a weaker condition on the moduli than $y$-smoothness, in distribution estimates for primes in arithmetic progressions. We obtain the order of magnitude of the count of these integers up to $x$, uniformly in $x$ and $y$, for every fixed natural number $i$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02699 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An extension of smooth numbers: multiple dense divisibility Sarajian, Garo Weingartner, Andreas Number Theory 11N25 The $i$-tuply $y$-densely divisible numbers were introduced by a Polymath project, as a weaker condition on the moduli than $y$-smoothness, in distribution estimates for primes in arithmetic progressions. We obtain the order of magnitude of the count of these integers up to $x$, uniformly in $x$ and $y$, for every fixed natural number $i$. |
| title | An extension of smooth numbers: multiple dense divisibility |
| topic | Number Theory 11N25 |
| url | https://arxiv.org/abs/2504.02699 |