Cyclotomic polynomials without using the zeros of $Y^n-1$

Gema M. Diaz-Toca, Henri Lombardi, Claude Quitté

This note aims to construct an ``intrinsic'' splitting field for the polynomial $Y^n-1$ over the rational field $\mathbf{Q}$, in a way that Gauss, Kummer, Kronecker and Bishop would hav…