Kirsten, Klaus, 1962-2015-09-042015-09-042015-082015-07-14August 201http://hdl.handle.net/2104/9459In this work, we provide the analytic continuation of the spectral zeta function associated with the one-dimensional regular Sturm-Liouville problem and the two-dimensional Laplacian on the annulus. In the one-dimensional setting, we consider general separated and coupled boundary conditions, and on the annulus we restrict our work to Dirichlet-Robin boundary conditions. In both cases, we use our results to calculate the coefficients of the asymptotic expansion of the associated heat kernel. In the one-dimensional case, we additionally use the analytically continued spectral zeta function to compute the determinant of the Sturm-Liouville operator.application/pdfenSpectral zeta function. Sturm-Liouville. Laplacian. WKB. Functional determinant. Heat kernel.Thesis2015-09-04Worldwide accessAccess changed 12/4/17