Simple proof of Chebotarev's theorem on roots of unity

TL;DR

This paper provides a straightforward proof of Chebotarev's theorem, demonstrating that all minors of a specific matrix formed by roots of unity are non-zero, which has implications in number theory and algebra.

Contribution

The paper introduces a simplified proof of Chebotarev's theorem on roots of unity minors, making the result more accessible and easier to understand.

Findings

All minors of the matrix $( ext{ω}^{ij})$ are non-zero for prime p.

The proof simplifies previous approaches to Chebotarev's theorem.

The result confirms the non-degeneracy of roots of unity matrices.

Abstract

We give a simple proof of Chebotarev's theorem: Let $p$ be a prime and $\omega $ a primitive $p$th root of unity. Then all minors of the matrix $(\omega^{ij})_{i,j=0}^{p-1}$ are non-zero.