Generalized factorials characterized by Dirichlet convolution
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914040963399680 |
|---|---|
| author | Ma, Wanli |
| author_facet | Ma, Wanli |
| contents | We extend A.B. Mingarelli's method for constructing generalized factorials. Our extension uses a pair of arithmetic functions $(x, y)$, where $x$ is superadditive. When $x$ is the identity function, our generalized factorial reduces to Mingarelli's. A result on the irrationality of the Euler constant within this framework is given. Using Dirichlet convolution, we characterize when two pairs $(α, β)$ and $(x, y)$ generate the same factorials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13354 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized factorials characterized by Dirichlet convolution Ma, Wanli Number Theory 11B65, 11Z05 We extend A.B. Mingarelli's method for constructing generalized factorials. Our extension uses a pair of arithmetic functions $(x, y)$, where $x$ is superadditive. When $x$ is the identity function, our generalized factorial reduces to Mingarelli's. A result on the irrationality of the Euler constant within this framework is given. Using Dirichlet convolution, we characterize when two pairs $(α, β)$ and $(x, y)$ generate the same factorials. |
| title | Generalized factorials characterized by Dirichlet convolution |
| topic | Number Theory 11B65, 11Z05 |
| url | https://arxiv.org/abs/2509.13354 |