Determinants of pseudo-Laplacians (Q390216)

Let \(X^d\) be a complete Riemannian manifold of dimension \(d = 2,3\) and \(P\) a point in \(X^d\). The authors present a comparison formula between \(\det (\Delta_{\alpha,P} - \lambda)\) and \(\det (\Delta - \lambda)\), for \(\lambda \in \mathbb{C} \setminus (\text{Spec}\; \Delta \cup \text{Spec}\; \Delta_{\alpha,P})\), where \(\Delta\) is the Laplace operator on \(X^d\) and \( \Delta_{\alpha,P}\) is the pseudo-Laplacian.