A Totient Function Associated with Variants of Groups
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911515538358272 |
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| author | Renshaw, James |
| author_facet | Renshaw, James |
| contents | Motivated by an application of semigroup variants to the discrete log problem in groups and related cryptographic applications, we introduce a new kind of totient function, related to both Euler's function and a generalisation of Euler's function introduced in 1869 by Schemmel. We focus on the problem of how to evaluate this function, and the number theory involved, while non-trivial and at times slightly technical, is reasonably accessible to a wide audience. It should also become clear that there are obvious generalisations of his new function that the interested reader might like to pursue. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_13939 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Totient Function Associated with Variants of Groups Renshaw, James Number Theory Group Theory 11A05, 11A25, 20A05, 20M10 Motivated by an application of semigroup variants to the discrete log problem in groups and related cryptographic applications, we introduce a new kind of totient function, related to both Euler's function and a generalisation of Euler's function introduced in 1869 by Schemmel. We focus on the problem of how to evaluate this function, and the number theory involved, while non-trivial and at times slightly technical, is reasonably accessible to a wide audience. It should also become clear that there are obvious generalisations of his new function that the interested reader might like to pursue. |
| title | A Totient Function Associated with Variants of Groups |
| topic | Number Theory Group Theory 11A05, 11A25, 20A05, 20M10 |
| url | https://arxiv.org/abs/2603.13939 |