What type of study is this?

This is a Quantitative Study study.

September 30, 2025Open Access

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

Key Points

Chebotarev's theorem confirms that every square submatrix is nonsingular, revealing structural properties of matrices.
The study proves the theorem for principal submatrices when the group order is the product of two distinct primes.
An uncertainty principle for cyclic groups of order pq emerges, linking matrix theory to group theory.
Applications of the theorem provide deep insights into the behavior of submatrices in algebraic structures.

Abstract

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.

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

Key Points

Abstract

Cite This Study

Also Consider

Also Consider