[en] We investigate the three-dimensional O(2) model on lattices of size 8³ to 160³ close to the critical point at zero magnetic field. We confirm explicitly the value of the critical coupling J_c found by Ballesteros et al. and estimate the universal values g_r and ξ/L. At criticality we study the finite size dependencies of the energy density ε and the specific heat C. We find that the nonsingular part of the specific heat C_ns is linearly dependent on 1/α. From the critical behaviour of the specific heat results at T ≠ T_c on the largest lattices we determine the universal amplitude ratio A⁺/A^-. The α-dependence of this ratio is close to the phenomenological relation A⁺/A^- = 1 - 4α