English

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 Yn1Y^n-1 over the rational field Q\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 Yn1Y^n-1 which would be given before demonstrating the irreducibility of the cyclotomic polynomial.

Keywords

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}
}