  Multiplicative logarithmic corrections frequently characterize critical
behaviour in statistical physics. Here, a recently proposed theory relating the
exponents of such terms is extended to account for circumstances which often
occur when the leading specific-heat critical exponent vanishes. Also, the
theory is widened to encompass the correlation function. The new relations are
then confronted with results from the literature and some new predictions for
logarithmic corrections in certain models are made.
