Zeta-Function Regularization

A method for assigning finite values to divergent spectral sums or infinite products by forming an associated zeta function ζ(s) (typically ζ(s)=∑ λ_i^{-s} for positive eigenvalues λ_i), analytically continuing ζ(s) to a neighborhood of a special point (often s=0), and defining regularized sums or determinants via values like ζ(0) or derivatives such as -ζ'(0).