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Generalized factorials characterized by Dirichlet convolution

2025/09/14 by Wan-Li Ma, Ma, Wanli
Computer Science · Mathematics · #11B65 #11Z05 #Advanced Mathematical Identities #FOS: Mathematics #Mathematical and Theoretical Analysis #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2509.13354

openalex publication_date 2025/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 (α, β) and (x, y) generate the same factorials.

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