Curious congruences for cyclotomic polynomials II

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.

7 pages