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arXiv · 2503.17701

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

Gema M. Diaz-Toca·Henri Lombardi·Claude Quitté
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Abstract

This note aims to construct an ``intrinsic'' splitting field for the polynomial $Y^n-1$ 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 $Y^n-1$ which would be given before demonstrating the irreducibility of the cyclotomic polynomial.

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Gema M. Diaz-Toca, Henri Lombardi, Claude Quitté. 2025-03-22. Cyclotomic polynomials without using the zeros of $Y^n-1$. https://arxiv.org/abs/2503.17701

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