| | |
| | |
Stat |
Members: 3643 Articles: 2'487'895 Articles rated: 2609
28 March 2024 |
|
| | | |
|
Article overview
| |
|
Distribution of determinant of matrices with restricted entries over finite fields | Le Anh Vinh
; | Date: |
13 Mar 2009 | Abstract: | 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 $d imes d$
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
$|mathcal{A}| = omega(q^{frac{d}{2d-1}})$, $dgeqslant 4$. When $q$ is a
prime and $mathcal{A}$ is a symmetric interval $[-H,H]$, we get the same
result for $dgeqslant 3$. This improves a result of Ahmadi and Shparlinski
(2007). | Source: | arXiv, 0903.2508 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |