Cyclotomic polynomials without using the zeros of Yⁿ-1

2025/03/22 by Diaz-Toca, Gema M., Lombardi, Henri, Quitté, Claude
#Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2503.17701

Abstract

This note aims to construct an ``intrinsic'' splitting field for the polynomial Yⁿ-1 over the rational field \bf Q, in a way that Gauss, Kummer, Kronecker and Bishop would have liked. Contrary to the usual presentations, our construction does not use any splitting field of Yⁿ-1 which would be given before demonstrating the irreducibility of the cyclotomic polynomial.

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