Related papers: Basic zeta functions and some applications in phys…
A technique for evaluating the electromagnetic Casimir energy in situations involving spherical or circular boundaries is presented. Zeta function regularization is unambiguously used from the start and the properties of Bessel and related…
We calculate the partition function of a harmonic oscillator with quasi-periodic boundary conditions using the zeta-function method. This work generalizes a previous one by Gibbons and contains the usual bosonic and fermionic oscillators as…
We give an introduction to the heat kernel technique and zeta function. Two applications are considered. First we derive the high temperature asymptotics of the free energy for boson fields in terms of the heat kernel expansion and zeta…
Spectral zeta functions $\zeta(s)$ for the massless scalar fields obeying the Dirichlet and Neumann boundary conditions on a surface of an infinite cylinder are constructed. These functions are defined explicitly in a finite domain of the…
This is an introductory set of lectures on elliptic differential operators and boundary problems, and their associated spectral functions. The role of zeta functions and traces of heat kernels in the regularization of Casimir energies is…
A pedagogical introduction to the heat kernel technique, zeta function and Casimir effect is presented. Several applications are considered. First we derive the high temperature asymptotics of the free energy for boson fields in terms of…
zeta-function methods are used to study the properties of the non-relativistic interacting Bose gas at finite temperature and density. Results for the ground state energy and pressure are obtained at both zero and finite temperature. The…
Spectral functions relevant in the context of quantum field theory under the influence of spherically symmetric external conditions are analysed. Examples comprise heat-kernels, determinants and spectral sums needed for the analysis of…
A simple method is proposed to construct the spectral zeta functions required for calculating the electromagnetic vacuum energy with boundary conditions given on a sphere or on an infinite cylinder. When calculating the Casimir energy in…
This paper generalizes Bass' work on zeta functions for uniform tree lattices. Using the theory of von Neumann algebras, machinery is developed to define the zeta function of a discrete group of automorphisms of a bounded degree tree. The…
We consider the variation of two fundamental types of zeta functions that arise in the study of both physical and analytical problems in geometric settings involving conical singularities. These are the Barnes zeta functions and the Bessel…
In this paper we explore the Zeta function arising from a small perturbation on a surface of revolution and the effect of this on the functional determinant and in the change of the Casimir energy associated with this configuration.
Fermi-Dirac and Bose-Einstein integral functions are of importance not only in quantum statistics but for their mathematical properties, in themselves. Here, we have extended these functions by introducing an extra parameter in a way that…
We consider the vacuum energy for a scalar field subject to a frequency dependent boundary condition. The effect of a frequency cut-off is described in terms of an {\it incomplete} $\zeta$-function. The use of the Debye asymptotic expansion…
On the one hand the Fermi-Dirac and Bose-Einstein functions have been extended in such a way that they are closely related to the Riemann and other zeta functions. On the other hand the Fourier transform representation of the gamma and…
Many examples of zeta functions in number theory and combinatorics are special cases of a construction in homotopy theory known as a decomposition space. This article aims to introduce number theorists to the relevant concepts in homotopy…
We define supersymmetric zeta functions and supersymmetric determinants, which can reveal spectral properties complementary to those captured by the supersymmetric indices. They play a crucial role in analyzing the Cardy-like behaviors of…
We explore the meromorphic structure of the $\zeta$-function associated to the boundary eigenvalue problem of a modified Sturm-Liouville operator subject to spectral dependent boundary conditions at one end of a segment of length $l$. We…
This paper discusses the simplest examples of spectral zeta functions, especially those associated with graphs, a subject which has not been much studied. The analogy and the similar structure of these functions, such as their parallel…
Partial zeta functions of algebraic varieties over finite fields generalize the classical zeta function by allowing each variable to be defined over a possibly different extension field of a fixed finite field. Due to this extra variation…