Curious congruences for cyclotomic polynomials II

2023/05/01 by Matsusaka, Toshiki, Shibukawa, Genki · 1 citation
#11A25 #11R18 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2305.00765

Abstract

We promote the recent research by Akiyama and Kaneko on the higher-order derivative values Φ_n^(k)(1) of the cyclotomic polynomials. This article focuses on Lehmer's explicit formula of Φ_n^(k)(1)/Φ_n(1) as a polynomial of the Euler and Jordan totient functions over ℚ. Then we prove Akiyama-Kaneko's conjecture that the polynomials have a specific simple factor.

Cited by

• Applications of Faà di Bruno's formula to partition traces

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