论文标题
$ s $ - 综合二次形式和均质动力学
$S$-integral quadratic forms and homogeneous dynamics
论文作者
论文摘要
令$ s = \ {\ infty \} \ cup s_f $是$ \ mathbb {q} $的有限位置。使用均匀的动力学，我们在三个或多个变量中建立了两个关于整体二次形式的新定量和明确的结果：第一个是$ s $ integral等价的标准。第二个确定了任何$ S $ integral Orthonal组的有限生成集。这两个定理都以$ s = \ {\ infty \} $扩展了H. Li和G. Margulis的结果 - 由多项式界限给出，以二次形式的系数的大小。
Let $S = \{ \infty \} \cup S_f$ be a finite set of places of $\mathbb{Q}$. Using homogeneous dynamics, we establish two new quantitative and explicit results about integral quadratic forms in three or more variables: The first is a criterion of $S$-integral equivalence. The second determines a finite generating set of any $S$-integral orthogonal group. Both theorems--which extend results of H. Li and G. Margulis for $S = \{ \infty\}$--are given by polynomial bounds on the size of the coefficients of the quadratic forms.
