Calculation of the multiplicative anomaly
  The functional determinant multiplicative anomaly, or defect, is more closely investigated and explicit forms for products of linear operators are produced. I also present formulae for the defect of products of second order operators in terms of that for just two of the factors and discuss the specific cases of the sphere and hemisphere. The difference of Neumann and Dirichlet quantities on the hemisphere is equal to that for spin-1/2 on the rim. This is proved generally. 
J.S. Dowker
hep-th math-ph math.AP math.FA math.MP math.SP