Curious congruences for cyclotomic polynomials II
| Autor: | Matsusaka, Toshiki, Shibukawa, Genki |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | We promote the recent research by Akiyama and Kaneko on the higher-order derivative values $\Phi_n^{(k)}(1)$ of the cyclotomic polynomials. This article focuses on Lehmer's explicit formula of $\Phi_n^{(k)}(1)/\Phi_n(1)$ as a polynomial of the Euler and Jordan totient functions over $\mathbb{Q}$. Then we prove Akiyama-Kaneko's conjecture that the polynomials have a specific simple factor. Comment: 7 pages |
| Databáze: | arXiv |
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