Zeta-regularized determinant

Summary

The zeta-regularized determinant of a positive elliptic operator is the regularized product of its eigenvalues, $\exp(-\zeta'(0))$, where $\zeta(s) = \sum \lambda^{-s}$ is its spectral zeta function. Ray and Singer introduced it for Laplacians in order to define analytic torsion. It is an instance of zeta function regularization and appears in string theory, quantum field theory and the geometry of determinant line bundles.