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arXiv · 2509.13354

Generalized factorials characterized by Dirichlet convolution

Wanli Ma
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Abstract

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 $(\alpha, \beta)$ and $(x, y)$ generate the same factorials.

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Wanli Ma. 2025-09-14. Generalized factorials characterized by Dirichlet convolution. https://arxiv.org/abs/2509.13354

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