论文标题
关于随机对称P-ADIC矩阵的等效类别的分布
On the distribution of equivalence classes of random symmetric p-adic matrices
论文作者
论文摘要
我们考虑根据$ \ mathbb {z} _p $在奇数primes $ p $上分配的独立条目的随机对称矩阵，并根据几种等价关系得出其规范形式的分布。我们为应用程序提供了一些示例，包括Bhargava，Cremona，Fisher，Jones和Keating的替代证明，并以$ \ Mathbb {Z} _P $具有非琐事的零次数的可能性。
We consider random symmetric matrices with independent entries distributed according to the Haar measure on $\mathbb{Z}_p$ for odd primes $p$ and derive the distribution of their canonical form with respect to several equivalence relations. We give a few examples of applications including an alternative proof for the result of Bhargava, Cremona, Fisher, Jones, and Keating on the probability that a random quadratic form over $\mathbb{Z}_p$ has a non-trivial zero.
