Coincidence rotations of the root lattice

The coincidence site lattices of the root lattice A 4 are considered, and the statistics of the corresponding coincidence rotations according to their indices is expressed in terms of a Dirichlet series generating function. This is possible via an embedding of A 4 into the icosian ring with its rich arithmetic structure, which recently [M Baake, M. Heuer, R.V. Moody, Similar sublattices of the root lattice A 4 , preprint arXiv:math.MG/0702448] led to the classification of the similar sublattices of A 4 .