Zeta-Regularized Determinant

A definition of a determinant for elliptic (typically positive) operators via the spectral zeta function: if {λ_j} are the positive eigenvalues, form ζ(s) = ∑ λ_j^{-s}, analytically continue ζ(s) to s=0 and define det' A = exp(−ζ'(0)). This regularizes the divergent infinite product of eigenvalues and produces meaningful spectral invariants.