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arXiv · 2202.10257

$S$-integral quadratic forms and homogeneous dynamics

Irving Calderón
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Abstract

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.

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Irving Calderón. 2022-02-21. $S$-integral quadratic forms and homogeneous dynamics. https://arxiv.org/abs/2202.10257

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