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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.13328 |
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| _version_ | 1866908344575328256 |
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| author | Kobin, Andrew |
| author_facet | Kobin, Andrew |
| contents | In this expository note, we revisit several classical arithmetic functions - namely Euler's totient function, the divisor sum functions and Dedekind's $ψ$-function - within a unifying algebraic framework that highlights their connections to geometry. This framework builds on prior work involving zeta functions and Möbius 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 $ψ$-function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13328 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Arithmetic Functions and Geometry Kobin, Andrew Number Theory 11A25, 11G25, 18F30 In this expository note, we revisit several classical arithmetic functions - namely Euler's totient function, the divisor sum functions and Dedekind's $ψ$-function - within a unifying algebraic framework that highlights their connections to geometry. This framework builds on prior work involving zeta functions and Möbius 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 $ψ$-function. |
| title | Arithmetic Functions and Geometry |
| topic | Number Theory 11A25, 11G25, 18F30 |
| url | https://arxiv.org/abs/2504.13328 |