# Séminaires : Séminaire Théorie des Nombres

 Equipe(s) : fa, tn, tga, Responsables : Marc Hindry, Bruno Kahn, Wieslawa Niziol, Cathy Swaenepoel Email des responsables : cathy.swaenepoel@imj-prg.fr Salle : Adresse : Description http://www.imj-prg.fr/tn/STN/stnj.html

 Orateur(s) Fei Xu - Capital Normal University, Titre Counting integral points in certain homogeneous spaces Date 09/12/2013 Horaire 14:00 à 16:00 Diffusion Résume The asymptotic formula of the number of integral points in non-compact symmetric homogeneous spaces of semi-simple simply connected algebraic groups is given by the average of the product of the number of local solutions twisted by the Brauer-Manin obstruction. As application, we will prove that the asymptotic formula of the number of integral matrices with a fixed irreducible characteristic polynomial over integers studied by Eskin-Mozes-Shah is equal to the product of the number of local integral solutions over all primes although the density function defined by Borovoi and Rudnick is not trivial in general. This is a joint work with Dasheng Wei. Salle Adresse