Related papers: Zeta function for perturbed surfaces of revolution
It is well-known that upper bounds for moments of the Riemann zeta function $\zeta(s)$ have implications for subconvexity bounds. In this paper we explore some implications in the opposite direction using functional analysis in the…
We study some of the interactions between the Fourier Transform and the Riemann zeta function (and Dirichlet-Dedekind-Hecke-Tate L-functions)
We express the zeta function associated to the Laplacian operator on $S^1_r\times M$ in terms of the zeta function associated to the Laplacian on $M$, where $M$ is a compact connected Riemannian manifold. This gives formulas for the…
Using the measured optical response and surface roughness topography as inputs, we perform realistic calculations of the combined effect of Casimir and electrostatic forces on the actuation dynamics of micro-electromechanical systems…
We consider the dynamical zeta functions of Selberg and Ruelle associated with the geodesic flow on a compact odd-dimensional hyperbolic manifold. These dynamical zeta functions are defined for a complex variable $s$ in some right-half…
The Casimir force provides a striking example of the effects of quantum fluctuations in a mesoscopic system. Because it arises from the objects' electromagnetic response, the necessary calculations in quantum field theory are most naturally…
The Casimir force between uncharged metallic surfaces originates from quantum mechanical zero point fluctuations of the electromagnetic field. We demonstrate that this quantum electrodynamical effect has a profound influence on the…
We study the connection between $\zeta $- and cutoff-regularized Casimir energies for scalar fields. We show that, in general, both regularization schemes lead to divergent contributions, and to finite parts which do not coincide. We…
The motion in the complex plane of the zeros to various zeta functions is investigated numerically. First the Hurwitz zeta function is considered and an accurate formula for the distribution of its zeros is suggested. Then functions which…
We introduce a Selberg type zeta function of two variables which interpolates several higher Selberg zeta functions. The analytic continuation, the functional equation and the determinant expression of this function via the Laplacian on a…
We use the definition of a star (or Moyal or twisted) product to give a phasespace definition of the $\zeta$-function. This allows us to derive new closed expressions for the coefficients of the heat kernel in an asymptotic expansion for…
In this work I study the Casimir effect caused by a charged and massive scalar field that violates Lorentz symmetry in an aether-like and CPT even manner, by direct coupling between the field derivatives and two fixed orthogonal unit…
We propose a field-theoretic interpretation of Ruelle zeta function, and show how it can be seen as the partition function for $BF$ theory when an unusual gauge fixing condition on contact manifolds is imposed. This suggests an alternative…
The Casimir effect for a scalar field in presence of delta-type potentials has been investigated for a long time in the case of surface delta functions, modelling semi-transparent boundaries. More recently Albeverio, Cacciapuoti, Cognola,…
For a divisor representing a function and another divisor representing a differential form on a normal surface singularity, there is a notion of motivic and topological zeta function. In this paper, given a finite morphism between two…
Some aspects of the multiplicative anomaly of zeta determinants are investigated. A rather simple approach is adopted and, in particular, the question of zeta function factorization, together with its possible relation with the…
The prototypical Casimir effect arises when a scalar field is confined between parallel Dirichlet boundaries. We study corrections to this when the boundaries themselves have apertures and edges. We consider several geometries: a single…
We define reduced zeta functions of Lie algebras, which can be derived from motivic zeta functions using the Euler characteristic. We show that reduced zeta functions of Lie algebras possessing a suitably well-behaved basis are easy to…
We explore the non-linear dynamics of two parallel periodically patterned metal surfaces that are coupled by the zero-point fluctuations of the electromagnetic field between them. The resulting Casimir force generates for asymmetric…
We compute the Casimir Energy of a spherical region using a Surface Impedance approach. We characterize the Surface Impedance of the boundary using plasma model. Exact analytical formulae are obtained by means of the zeta function…