Determinants of Laplace-like operators on Riemann surfaces
Laplacian type operators are defined, acting on sections of parametrized tensor bundles over compact Riemann surfaces. Determinants of these operators are defined via the usual regularization, from analytic continuation of the zeta function. These determinants are then calculated by an inductive procedure, relying upon Selberg's zeta function. The answer differs in some respects from earlier direct calculations using Selberg's trace formula. The authors proceed to clarify the reasons for these discrepancies.
scientific article; zbMATH DE number 4155528