Cyclotomic polynomials without using the zeros of $Y^n-1$
Number Theory
2025-03-25 v1 Commutative Algebra
Abstract
This note aims to construct an ``intrinsic'' splitting field for the polynomial over the rational field , 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 which would be given before demonstrating the irreducibility of the cyclotomic polynomial.
Cite
@article{arxiv.2503.17701,
title = {Cyclotomic polynomials without using the zeros of $Y^n-1$},
author = {Gema M. Diaz-Toca and Henri Lombardi and Claude Quitté},
journal= {arXiv preprint arXiv:2503.17701},
year = {2025}
}