Related papers: Kabat's Surface Terms in the Zeta-Function approac…
Using the cohomology theory of Dwork, as developed by Adolphson and Sperber, we exhibit a deterministic algorithm to compute the zeta function of a nondegenerate hypersurface defined over a finite field. This algorithm is particularly…
We present various improvements to the deformation method for computing the zeta function of smooth projective hypersurfaces over finite fields using $p$-adic cohomology. This includes new bounds for the $p$-adic and $t$-adic precisions…
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 review the construction of the universal Hamilton-Jacobi counterterm for dilaton gravity in two dimensions, derive the corresponding result in the Cartan formulation and elaborate further upon black hole thermodynamics and semi-classical…
A coarse-grained version of the effective action is used to study the thermodynamics of black holes, interpolating from largest to smallest masses. The physical parameter of the black hole are linked to the running couplings by…
Some general properties of local $\zeta$-function procedures to renormalize some quantities in $D$-dimensional (Euclidean) Quantum Field Theory in curved background are rigorously discussed for positive scalar operators $-\Delta + V(x)$ in…
We consider an Einstein-Hilbert-Dilaton action for gravity coupled to various types of Abelian and non-Abelian gauge fields in a spatially finite system. These include Yang-Mills fields and Abelian gauge fields with three and four-form…
The thermodynamics of ``horizon brightened acceleration radiation'' (HBAR), due to a random atomic cloud freely falling into a black hole in a Boulware-like vacuum, is shown to mimic the thermodynamics of the black hole itself. The…
We use the solutions of the noncommutative Wheeler-De Witt equation arising from a Kantowski-Sachs cosmological model to compute thermodynamic properties of the Schwarzschild black hole. We show that the noncommutativity in the momentum…
A new approach to black hole thermodynamics is proposed in Loop Quantum Gravity (LQG), by defining a new black hole partition function, followed by analytic continuations of Barbero-Immirzi parameter to $\gamma\in i\mathbb{R}$ and…
Thermodynamics of extended gravity static spherically symmetric black hole solutions is investigated. The energy issue is discussed making use of the derivation of Clausius relation from equations of motion, evaluating the black hole…
We study the Ruelle zeta function at zero for negatively curved oriented surfaces with boundary. At zero, the zeta function has a zero and its multiplicity is shown to be determined by the Euler characteristic of the surface. This is shown…
It is shown that the canonical problem of classical statistical thermodynamics, the computation of the partition function, is in the case of +/-J Ising spin glasses a particular instance of certain simple sums known as quadratically signed…
The aim of this article is to illustrate, on the example of Dwork hypersurfaces, how the study of the representation of a finite group of automorphisms of a hypersurface in its etale cohomology allows to factor its zeta function.
The on-shell gravitational action and the boundary stress tensor are essential ingredients in the study of black hole thermodynamics. We employ the Hamilton-Jacobi method to calculate the boundary counterterms necessary to remove the…
We identify a partition-theoretic generalization of Riemann zeta function and the equally positive integer-indexed harmonic sums at infinity, to obtain the generating function and the integral representations of the latter. The special…
The Hamiltonian thermodynamics formalism is applied to the general $d$-dimensional Reissner-Nordstr\"om-anti-de Sitter black hole with spherical, planar, and hyperbolic horizon topology. After writing its action and performing a Legendre…
We relate the heat kernel and quasinormal mode methods of computing the 1-loop partition function of arbitrary spin fields on a rotating (Euclidean) BTZ background using the Selberg zeta function associated with $\mathbb{H}^{3}/\mathbb{Z}$,…
We present a general solution for correlators of external boundary operators in black hole states of Jackiw-Teitelboim gravity. We use the Hilbert space constructed using the particle-with-spin interpretation of the Jackiw-Teitelboim…
We study correlation functions of coset constructions by utilizing the method of gauge dressing. As an example we apply this method to the minimal models and to the Witten 2D black hole. We exhibit a striking similarity between the latter…