Anomalies and analytic torsion on hyperbolic manifolds

The global additive and multiplicative properties of the Laplacian on j-for ms and related zeta functions are analyzed. The explicit form of zeta funct ions on a product of closed oriented hyperbolic manifolds Gamma\H-d and of the multiplicative anomaly are derived. We also calculate in an explicit fo rm the analytic torsion associated with a connected sum of such manifolds. (C) 1999 American Institute of Physics. [S0022-2488(99)01407-3].