论文标题
矩阵的分布在$ \ mathbb {f} _q [x] $上
Distributions of Matrices over $\mathbb{F}_q[x]$
论文作者
论文摘要
在本文中，我们计算矩阵$ a =（a_ {i，j}）\ in \ Mathcal {o} \ subset mat_ {n \ times n}（\ Mathbb {f} _q [x] _q [x]）$ t $，和$ \ mathcal {o} $ a $ gl_n（\ mathbb {f} _q [x]）$的给定轨道。通过一个基本参数，我们表明上述数字恰好是$ \＃gl_n（\ mathbb {f} _Q）\ cdot q^{（n-1）（nk-t）} $。该公式在$ \ mathbb {f} _q [x] $上给出了一个等式分布结果，该结果以$ \ mathbb {z} $以前的结果为模拟。
In this paper, we count the number of matrices $A = (A_{i,j} )\in \mathcal{O} \subset Mat_{n\times n}(\mathbb{F}_q[x])$ where $deg(A_{i,j})\leq k, 1\leq i,j\leq n$, $deg(\det A) = t$, and $\mathcal{O}$ a given orbit of $GL_n(\mathbb{F}_q[x])$. By an elementary argument, we show that the above number is exactly $\# GL_n(\mathbb{F}_q)\cdot q^{(n-1)(nk-t)}$. This formula gives an equidistribution result over $\mathbb{F}_q[x]$ which is an analogue, in strong form, of a result over $\mathbb{Z}$ before.
