The Chebotarev theorem on roots of unity was originally a conjecture made by Ostrowski in the context of lacunary series.
Chebotarev was the first to prove it, in the 1930s. This proof involves tools from Galois theory and pleased Ostrowski, who made comments arguing that it "does meet the requirements of mathematical esthetics".Stevenhagen et al., 1996 Several proofs have been proposed since,P.E. Frenkel, 2003 and it has even been discovered independently by Dieudonné.J. Dieudonné, 1970
Statement
Let be a matrix with entries , where . If is prime then any minor of is non-zero.
Equivalently, all submatrices of a DFT matrix of prime length are invertible.
Applications In signal processing,Candès, Romberg, Tao, 2006 the theorem was used by T. Tao to extend the uncertainty principle.T. Tao, 2003
Notes
References