Related papers: Twisted determinants on higher genus Riemann surfa…

The bosonization equivalence between the 2-dimensional Dirac and Laplacian operators can be used to derive new interesting identities involving Theta functions. We use these formulae to compute the multiloop partition function of the…

We present gluing formulas for zeta regularized determinants of Dolbeault laplacians on Riemann surfaces. These are expressed in terms of determinants of associated operators on surfaces with boundary satisfying local elliptic boundary…

Let $X$ be a Riemann surface of genus $g\ge 1$ endowed with a flat conical metric $m$ and let ${\rm det}\,\Delta$ be the $\zeta$-regularized determinant of the Friedrichs Laplacian on $(X,m)$. We derive variational formulas for ${\rm…

We find an explicit expression for the zeta-regularized determinant of (the Friedrichs extension) of the Laplacian on a compact Riemann surface of genus one with conformal metric of curvature $1$ having a single conical singularity of angle…

We investigate the behaviour of the regularized determinant of the Laplace-Beltrami operator on compact hyperbolic surfaces when the genus goes to infinity. We show that for all popular models of random surfaces, with high probability as…

Compact polyhedral surfaces (or, equivalently, compact Riemann surfaces with conformal flat conical metrics) of an arbitrary genus are considered. After giving a short self-contained survey of their basic spectral properties, we study the…

The goal of this paper is to compute the zeta function determinant for the massive Laplacian on Riemann caps (or spherical suspensions). These manifolds are defined as compact and boundaryless $D-$dimensional manifolds deformed by a…

We prove a formula for the determinant of Laplacian on an arbitrary compact polyhedral surface of genus one. This formula generalizes the well-known Ray-Singer result for a flat torus. A special case of flat conical metrics given by the…

The odd signature operator is a Dirac operator which acts on the space of differential forms of all degrees and whose square is the usual Laplacian. We extend the result of [15] to prove the gluing formula of the zeta-determinants of…

We study two types of regularizations of the determinant of Laplacian on Riemann manifold from the viewpoint of resurgence theory. One is the formal logarithmic derivative of the determinant, and the other is its exponential deformation.…

In this note we pursue a discrete analogue of a celebrated theorem by Osgood, Phillips and Sarnak, which states that in a fixed conformal class of Riemannian metrics of fixed volume on a closed Riemann surface, the zeta-determinant of the…

In this paper we discuss the BFK type gluing formula for zeta-determinants of Laplacians with respect to the Robin boundary condition on a compact Riemannian manifold. As a special case, we discuss the gluing formula with respect to the…

We study the asymptotics of the determinant of Laplacian on a translation surface (a compact Riemann surface equipped with a conformal flat conical metric with trivial holonomy) of genus g with 2g-2 conical points of angle 4\pi as two…

We study functional determinants for Dirac operators on manifolds with boundary. We give, for local boundary conditions, an explicit formula relating these determinants to the corresponding Green functions. We finally apply this result to…

We show in a unified manner that the factorization method describes completely the $L^2$-eigenspaces associated to the discrete part of the spectrum of the twisted Laplacian on constant curvature Riemann surfaces. Subclasses of two variable…

On an open manifold, the spaces of metrics or connections of bounded geometry, respectively, split into an uncountable number of components. We show that for a pair of metrics or connections, belonging to the same component, relative…

For $\Pi \subset \mathbb{R}^2$ a connected, open, bounded set whose boundary is a finite union of disjoint polygons whose vertices have integer coordinates, the logarithm of the discrete Laplacian on $L\Pi \cap \mathbb{Z}^2$ with Dirichlet…

We discuss a specific class of regular-singular Laplace-type operators with matrix coefficients. Their zeta determinants were studied by K. Kirsten, P. Loya and J. Park on the basis of the Contour integral method, with general boundary…

This paper presents a Meyer-Vietoris type gluing formula for a conformal invariant of a Riemannian surface with boundary that is defined by the determinant of the Dirichlet-to-Neumann operator. The formula is used to bound the asymptotics…

Using the overlap formulation, we calculate the fermionic determinant on the lattice for chiral fermions with twisted boundary conditions in two dimensions. When the lattice spacing tends to zero we recover the results of the usual…