Eisenstein series and equidistribution of Lebesgue probability measures on compact leaves of the horocycle foliations of Bianchi 3-orbifolds

Inspired by the works of Zagier, we study the probability measures $ u(t)$ with support on the flat tori which are the compact orbits of the maximal unipotent subgroup acting holomorphically on the positive orthonormal frame bundle $mathcal{F}({M}_D)$ of 3-dimensional hyperbolic Bianchi orbifolds ${M}_D=mathbb{H}^3/widetilde{Gamma}_D$, of finite volume and with only one cusp. Here $Gamma_D=PSL(2, mathcal{O})$, where $mathcal{O}$ is the ring of integers of an imaginary quadratic field of class number one.