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arXiv · 1712.05503

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

Waseem Alass·Sumaia Saad Eddin
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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, M\"obius, divisor, and Jordan totient functions.

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Waseem Alass, Sumaia Saad Eddin. 2017-12-15. Weighted averages of arithmetic functions over regular integers modulo $n$. https://arxiv.org/abs/1712.05503

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