Multi angle Counting and equidistribution of integral representations by quadratic norm forms in positive characteristic?
Auteurs : Paulin, Frédéric (Auteur de la Conférence)
CIRM (Editeur )
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Résumé : In this talk, we will prove the projective equidistribution of integral representations by quadratic norm forms in positive characteristic, with error terms, and deduce asymptotic counting results of these representations. We use the ergodic theory of lattice actions on Bruhat-Tits trees, and in particular the exponential decay of correlation of the geodesic flow on trees for Hölder variables coming from symbolic dynamics techniques.Codes MSC :
11J61 - Approximation in non-Archimedean valuations
20E08 - Groups acting on trees
20G25 - Linear algebraic groups over local fields and their integers
37A25 - Ergodicity, mixing, rates of mixing
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)