On the denominators of harmonic numbers. IV
| Title: | On the denominators of harmonic numbers. IV |
|---|---|
| Authors: | Wu, Bing-Ling, Yan, Xiao-Hui |
| Source: | Comptes Rendus. Mathématique, Vol 360, Iss G1, Pp 53-57 (2022) |
| Publisher Information: | Académie des sciences, 2022. |
| Publication Year: | 2022 |
| Collection: | LCC:Mathematics |
| Subject Terms: | harmonic numbers, least common multiples, upper asymptotic density, Mathematics, QA1-939 |
| More Details: | Let $\mathcal{L}$ be the set of all positive integers $n$ such that the denominator of $1+1/2+\cdots +1/n$ is less than the least common multiple of $1, 2, \dots , n$. In this paper, under a certain assumption on linear independence, we prove that the set $\mathcal{L}$ has the upper asymptotic density $1$. The assumption follows from Schanuel’s conjecture. |
| Document Type: | article |
| File Description: | electronic resource |
| Language: | English French |
| ISSN: | 1778-3569 |
| Relation: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.282/; https://doaj.org/toc/1778-3569 |
| DOI: | 10.5802/crmath.282 |
| Access URL: | https://doaj.org/article/dbe0a600aa714edf8842b3675171c813 |
| Accession Number: | edsdoj.be0a600aa714edf8842b3675171c813 |
| Database: | Directory of Open Access Journals |
| ISSN: | 17783569 |
|---|---|
| DOI: | 10.5802/crmath.282 |
| Published in: | Comptes Rendus. Mathématique |
| Language: | English French |