Chebotarev's theorem for groups of order $pq$ and an uncertainty principle
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916924088123392 |
|---|---|
| author | Loukaki, Maria |
| author_facet | Loukaki, Maria |
| contents | Let $p$ be a prime number and $ζ_p$ a primitive $p$-th root of unity. Chebotarev's theorem states that every square submatrix of the $p \times p$ matrix $(ζ_p^{ij})_{i,j=0}^{p-1}$ is non-singular. In this paper we prove the same for principal submatrices of $(ζ_n^{ij})_{i,j=0}^{n-1}$, when $n=pr$ is the product of two distinct primes, and $p$ is a large enough prime that has order $r-1$ in $\mathbf{Z}_r^*$. As an application, an uncertainty principle for cyclic groups of order $n$ is established when $n=pr$ as described above. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08600 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chebotarev's theorem for groups of order $pq$ and an uncertainty principle Loukaki, Maria Number Theory Let $p$ be a prime number and $ζ_p$ a primitive $p$-th root of unity. Chebotarev's theorem states that every square submatrix of the $p \times p$ matrix $(ζ_p^{ij})_{i,j=0}^{p-1}$ is non-singular. In this paper we prove the same for principal submatrices of $(ζ_n^{ij})_{i,j=0}^{n-1}$, when $n=pr$ is the product of two distinct primes, and $p$ is a large enough prime that has order $r-1$ in $\mathbf{Z}_r^*$. As an application, an uncertainty principle for cyclic groups of order $n$ is established when $n=pr$ as described above. |
| title | Chebotarev's theorem for groups of order $pq$ and an uncertainty principle |
| topic | Number Theory |
| url | https://arxiv.org/abs/2412.08600 |