Équidistribution, comptage et approximation par irrationnels quadratiques

Details Équidistribution, comptage et approximation par irrationnels quadratiques Équidistribution, comptage et approximation par irrationnels quadratiques

2010-04-03

arxiv.org/abs/1004.0454v2

Mathematics

Dynamical Systems

41 pages, 5 figures. v2: a macro problem while first compiled by ArXiv has been corrected

Scientific paper

Let $M$ be a finite volume hyperbolic manifold, we show the equidistribution in $M$ of the equidistant hypersurfaces to a finite volume totally geodesic submanifold $C$. We prove a precise asymptotic on the number of geodesic arcs of lengths at most $t$, that are perpendicular to $C$ and to the boundary of a cuspidal neighbourhood of $M$. We deduce from it counting results of quadratic irrationals over $\QQ$ or over imaginary quadratic extensions of $\QQ$, in given orbits of congruence subgroups of the modular groups.

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