Article
| Title: | DDT theorem over $k$-free numbers in short intervals (English) |
| Author: | Liu, Ruiyang |
| Author: | Wen, Tingting |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 76 |
| Issue: | 1 |
| Year: | 2026 |
| Pages: | 335-347 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $k\geq 3$ be an integer. We investigate the distribution of divisors of $k$-free numbers using the Selberg-Delange method. We establish that the Cesàro mean of distribution functions converges uniformly to the arcsine law in short intervals. This generalizes the Deshouillers-Dress-Tenenbaum (DDT) theorem. (English) |
| Keyword: | arcsine law |
| Keyword: | Selberg-Delange method |
| Keyword: | $k$-free number |
| Keyword: | Dirichlet series |
| MSC: | 11M06 |
| MSC: | 11N37 |
| MSC: | 11N60 |
| DOI: | 10.21136/CMJ.2026.0382-25 |
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| Date available: | 2026-03-13T09:35:21Z |
| Last updated: | 2026-03-16 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153575 |
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