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arXiv · 2305.00765

Curious congruences for cyclotomic polynomials II

Toshiki Matsusaka·Genki Shibukawa
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Abstract

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.

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Toshiki Matsusaka, Genki Shibukawa. 2023-05-01. Curious congruences for cyclotomic polynomials II. https://arxiv.org/abs/2305.00765

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