A Totient Function Associated with Variants of Groups

Fuente: arXiv
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Main Author: Renshaw, James
Format: Preprint
Published: 2026
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_version_ 1866911515538358272
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