  We calculate numerically the logarithmic contribution to the entanglement
entropy of a cylindrical region in three spatial dimensions for both, free
scalar and Dirac fields. The coefficient is universal and proportional to the
type $c$ conformal anomaly in agreement with recent analytical predictions. We
also calculate the mass corrections to the entanglement entropy for scalar and
Dirac fields in a disk. These apparently unrelated problems make contact
through the dimensional reduction procedure valid for free fields whereby the
entanglement entropy for the cylinder can be calculated as an integral over
masses of the disk entanglement entropies. Coming from the same numerical
evaluation in the lattice, each coefficient is cross checked by the other,
testing in this way the two results simultaneously.
