Chebotarev's theorem for cyclic groups of order pq$pq$ and an uncertainty principle

Abstract Let be a prime number and a primitive th root of unity. Chebotarev's theorem states that every square submatrix of the matrix is nonsingular. In this paper, we prove the same for principal submatrices of , when is the product of two distinct primes, and is a large enough prime that has order in . As an application, an uncertainty principle for cyclic groups of order is established when as described above.