Generalizations of Euler's $φ$-function with respect to systems of polynomials of several variables
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915464385396736 |
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| author | Csizmazia, Norbert Tóth, László |
| author_facet | Csizmazia, Norbert Tóth, László |
| contents | We introduce a new generalization of Euler's $φ$-function associated with a system of polynomials of several variables. We reprove by a short direct approach certain known related identities, and study some other special cases that do not appear in the literature. We also discuss the unitary analogues of these functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19103 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalizations of Euler's $φ$-function with respect to systems of polynomials of several variables Csizmazia, Norbert Tóth, László Number Theory Primary 11A25, Secondary 11A05, 11A07, 11N37 We introduce a new generalization of Euler's $φ$-function associated with a system of polynomials of several variables. We reprove by a short direct approach certain known related identities, and study some other special cases that do not appear in the literature. We also discuss the unitary analogues of these functions. |
| title | Generalizations of Euler's $φ$-function with respect to systems of polynomials of several variables |
| topic | Number Theory Primary 11A25, Secondary 11A05, 11A07, 11N37 |
| url | https://arxiv.org/abs/2508.19103 |