论文标题
具有$ k $二维的整体二次形式的密度完全全向子空间
The density of integral quadratic forms having a $k$-dimensional totally isotropic subspace
论文作者
论文摘要
我们研究了$ {\ mathbb {z}} [x_1，...，...，x_n] $中的随机二次形式形式的概率完全具有给定维度的各向同性子空间。我们表明，这种全球概率是局部概率的产物。我们的主要结果计算了这些二次形式的这些局部概率在$ p $ -ADIC上。我们获得的公式是$ p $不变的合理功能，替换$ p \ p \ mapsto 1/p $。
We investigate the probability that a random quadratic form in ${\mathbb{Z}}[x_1,...,x_n]$ has a totally isotropic subspace of a given dimension. We show that this global probability is a product of local probabilities. Our main result computes these local probabilities for quadratic forms over the $p$-adics. The formulae we obtain are rational functions in $p$ invariant upon substituting $p \mapsto 1/p$.
