%0 Journal Article
%T Counting and equidistribution in Heisenberg groups
%A Jouni Parkkonen
%A Fr¨¦d¨¦ric Paulin
%J Mathematics
%D 2014
%I arXiv
%X We strongly develop the relationship between complex hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on complex hyperbolic spaces, especially in dimension $2$. We prove a Mertens' formula for the integer points over a quadratic imaginary number fields $K$ in the light cone of Hermitian forms, as well as an equidistribution theorem of the set of rational points over $K$ in Heisenberg groups. We give a counting formula for the cubic points over $K$ in the complex projective plane whose Galois conjugates are orthogonal and isotropic for a given Hermitian form over $K$, and a counting and equidistribution result for arithmetic chains in the Heisenberg group when their Cygan diameter tends to $0$.
%U http://arxiv.org/abs/1402.7225v2