  The leading mean-field critical behaviour of $\phi^4_4$-theory is modified by
multiplicative logarithmic corrections. We analyse these corrections both
analytically and numerically. In particular we present a finite-size scaling
theory for the Lee-Yang zeroes and temperature zeroes, both of which exhibit
logarithmic corrections. On lattices from size $8^4$ to $24^4$, Monte-Carlo
cluster methods and multi-histogram techniques are used to determine the
partition function zeroes closest to the critical point. Finite-size scaling
behaviour is verified and the logarithmic corrections are found to be in good
agreement with our analytical predictions.
