Équidistribution non archimédienne et actions de groupes sur les arbres = Non-Archimedean equidistribution and group actions on trees
Broise-Alamichel, A., Parkkonen, J., & Paulin, F. (2016). Équidistribution non archimédienne et actions de groupes sur les arbres = Non-Archimedean equidistribution and group actions on trees. Comptes Rendus Mathematique, 354(10), 971-975. https://doi.org/10.1016/j.crma.2016.08.001
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Comptes Rendus MathematiqueDate
2016Copyright
© 2016 Académie des sciences. Publié par Elsevier Masson SAS. Cet article est publié en
Open Access sous licence CC BY-NC-ND.
We give equidistribution results of elements of function fields over finite fields, and of quadratic irrationals over these fields, in their completed local fields. We deduce these results from equidistribution theorems of common perpendiculars in quotients of trees by lattices in their automorphism groups, proved by using ergodic properties of the discrete geodesic flow. Nous donnons des résultats d'équidistribution d'éléments de corps de fonctions sur des corps finis, et d'irrationnels quadratiques sur ces corps, dans leurs corps locaux complétés. Nous déduisons ces résultats de théorèmes d'équidistribution de perpendiculaires communes dans des quotients d'arbres par des réseaux de leur groupe d'automorphismes, démontrés à l'aide de propriétés ergodiques du flot géodésique discret.
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Except where otherwise noted, this item's license is described as © 2016 Académie des sciences. Publié par Elsevier Masson SAS. Cet article est publié en
Open Access sous licence CC BY-NC-ND.
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