Distribution of determinant of matrices with restricted entries over finite fields
| dc.creator | Vinh, Le Anh | |
| dc.date | 2009-03-13 | |
| dc.date.accessioned | 2026-07-07T12:52:40Z | |
| dc.date.available | 2026-07-07T12:52:40Z | |
| dc.description | For a prime power $q$, we study the distribution of determinent of matrices with restricted entries over a finite field $\mathbbm{F}_q$ of $q$ elements. More precisely, let $N_d (\mathcal{A}; t)$ be the number of $d \times d$ matrices with entries in $\mathcal{A}$ having determinant $t$. We show that \[ N_d (\mathcal{A}; t) = (1 + o (1)) \frac{|\mathcal{A}|^{d^2}}{q}, \] if $|\mathcal{A}| = ω(q^{\frac{d}{2d-1}})$, $d\geqslant 4$. When $q$ is a prime and $\mathcal{A}$ is a symmetric interval $[-H,H]$, we get the same result for $d\geqslant 3$. This improves a result of Ahmadi and Shparlinski (2007). | |
| dc.description | Journal of Combinatorics and Number Theory (to appear) | |
| dc.identifier | https://arxiv.org/abs/0903.2508 | |
| dc.identifier | http://arxiv.org/abs/0903.2508 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223370 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 11C20, 11T23 | |
| dc.title | Distribution of determinant of matrices with restricted entries over finite fields | |
| dc.type | text |