  An expression for the functional determinant on a sphere for a massive
(scalar) field derived by Denef, Hartnoll and Sachdev using quasinormal modes
is shown to exist already in the literature together with the multiplicative
anomaly interpretation. The relevant expressions are outlined and several
equivalent versions are given. The variation with mass is determined
numerically.
  As an application of the derived formulae, the Hartle--Hawking probability of
the Universe (via the dS/CFT correspondance) is recomputed. Agreement is found
with Anninos, Denef and Harlow. The calculation is extended to all (odd)
dimensions. I also compute the wave function which reveals an interesting
feature.
