Using two sets of high-precision Monte Carlo data for the two-dimensio
nal XY model in the Villain formulation on square L x L lattices, the
scaling behavior of the susceptibility chi and correlation length xi a
t the Kosterlitz-Thouless phase transition is analyzed with emphasis o
n multiplicative logarithmic corrections (lnL)(-2r) in the finite-size
scaling region and (in xi)(-2r) in the high-temperature phase near cr
iticality, respectively. By analyzing the susceptibility at criticalit
y on lattices of size up to 512(2) we obtain r=-0.0270(10), in agreeme
nt with recent work of Kenna and Irving on the finite-size scaling of
Lee-Yang zeros in the cosine formulation of the XY model. By studying
susceptibilities ana correlation lengths up to xi approximate to 140 i
n the high-temperature phase, however, we arrive at quite a different
estimate of r=0.0560(17), which is in good agreement with recent analy
ses of thermodynamic Monte Carlo data and high-temperature series expa
nsions of the cosine formulation.