Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2412.08600 |
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Inhaltsangabe:
- 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.