Arithmetic Functions and Geometry

Andrew Kobin

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arXiv · 2504.13328

Arithmetic Functions and Geometry

Andrew Kobin

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Abstract

In this expository note, we revisit several classical arithmetic functions - namely Euler's totient function, the divisor sum functions and Dedekind's $\psi$-function - within a unifying algebraic framework that highlights their connections to geometry. This framework builds on prior work involving zeta functions and M\"obius inversion. While our main goal is to provide a clear context for similar constructions in the future, we also make an original observation regarding Dedekind's $\psi$-function.

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Andrew Kobin. 2025-04-17. Arithmetic Functions and Geometry. https://arxiv.org/abs/2504.13328

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