Weighted averages of arithmetic functions over regular integers modulo $n$

Abstract

We investigate weighted averages of arithmetic functions over regular integers modulo $n$, extending previous identities of Kiuchi and Matsuoka. We establish general transformation formulas for the associated partial sums corresponding to arbitrary arithmetic functions. These formulas provide a unified framework for deriving asymptotic results. As applications, we obtain explicit asymptotic formulas for weighted averages involving several classical multiplicative functions, including the identity, Möbius, divisor, and Jordan totient functions.

18 pages

References in corpus (1)

• Some remarks on regular integers modulo $n$