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Arithmetic Functions' Bell Series 📂Number Theory

Arithmetic Functions' Bell Series

Definition 1

Given the arithmetic function ff and prime number pp, the following fp(x)f_{p}(x) is defined as the Bell series of ff modulo pp. fp(x):=n=0f(pn)xn f_{p}(x) := \sum_{n=0}^{\infty} f \left( p^{n} \right) x^{n}


  1. Apostol. (1976). Introduction to Analytic Number Theory: p42. ↩︎