Principal minors of Fourier matrices of square-free order

2025/05/30 by Caragea, Andrei, Lee, Dae Gwan, Malikiosis, Romanos +1
#11R18 #42A99 #42C15 #FOS: Mathematics #Functional Analysis (math.FA) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.24326

Abstract

Chebotarev's theorem on roots of unity states that all minors of a Fourier matrix are non-zero if and only if the order of the matrix is prime. We establish cases in which all principal minors of Fourier matrices of square-free order are non-zero. In a subsequent paper we discuss the case of composites containing squares.

Citations

• Simple proof of Chebotarev's theorem on roots of unity
• An uncertainty principle for cyclic groups of prime order

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