Author:
PARKKONEN JOUNI,PAULIN FRÉDÉRIC
Abstract
Abstract
We develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension 2. We prove a Mertens counting formula for the rational points over a definite quaternion algebra A over
${\mathbb{Q}}$
in the light cone of quaternionic Hermitian forms, as well as a Neville equidistribution theorem of the set of rational points over A in quaternionic Heisenberg groups.
Publisher
Cambridge University Press (CUP)
Reference46 articles.
1. Stationary measures and invariant subsets of homogeneous spaces II;Y.;J. Amer. Math. Soc.,2013
2. Local limit theorems and equidistribution of random walks on the Heisenberg group;E.;Geom. Funct. Anal.,2005
3. [Phi] Z., Philippe . Invariants globaux des variétés hyperboliques quaternioniques. Université de Bordeaux (Dec. 2016) https://tel.archives-ouvertes.fr/tel-01661448.
4. [Rei] I., Reiner . Maximal Orders, (Academic Press, 1972).
5. [She] T., Shemanske . The arithmetics and combinatorics of buidings for ${{Sp}}_n$ . Trans. Amer. Math. Soc 359 (2007), 3409–3423.
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献