2007/09/17 by Antonin Guilloux, Guilloux, Antonin
Mathematics · #11E12 #20G35 #37A45 #37K60 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)
paper · doi:10.48550/arxiv.0709.2603
openalex publication_date 2007/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study some subsets of rational points in an algebraic groups defined by open conditions on their projection in the finite adeles points. Using adelic mixing we are able to prove an equidistribution's result for the projection of these sets in the real points. As an application, we study the existence and the repartition of rational unitary matrices having a given denominator. We prove a local-global principle for this problem and the equirepartition of the sets of denominator n-matrices when they are not empty. Then we study the more complicated case of non simply-connected groups applying it to quadratic forms.