  We investigate the three-dimensional O(2) model near the critical point by
Monte Carlo simulations and calculate the major universal amplitude ratios of
the model. The ratio U_0=A+/A- is determined directly from the specific heat
data at zero magnetic field. The data do not, however, allow to extract an
accurate estimate for alpha. Instead, we establish a strong correlation of U_0
with the value of alpha used in the fit. This numerical alpha-dependence is
given by A+/A- = 1 -4.20(5) alpha + O(alpha^2). For the special alpha-values
used in other calculations we find full agreement with the corresponding ratio
values, e. g. that of the shuttle experiment with liquid helium. On the
critical isochore we obtain the ratio xi+/xi-_T=0.293(9), and on the critical
line the ratio xi_T^c/xi_L^c=1.957(10) for the amplitudes of the transverse and
longitudinal correlation lengths. These two ratios are independent of the used
alpha or nu-values.
