Coincidence rotations of the root lattice A4A4

The coincidence site lattices of the root lattice A4A4 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 A4A4 into the icosian ring with its rich arithmetic structure, which recently [M Baake, M. Heuer, R.V. Moody, Similar sublattices of the root lattice A4A4, preprint arXiv:math.MG/0702448] led to the classification of the similar sublattices of A4A4.