$S$-integral quadratic forms and homogeneous dynamics

Autor:	Calderón, Irving
Rok vydání:	2022
Předmět:	Mathematics - Number Theory Mathematics - Dynamical Systems 11E12 37A17 (Primary) 11E08 11H55 37A25 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: We add in the introduction a discussion of the extension of the results to any number field. Some misprints corrected
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2202.10257 Zobrazit plný text záznamu View this record from Arxiv