Related papers: The Ruelle zeta function at zero for nearly hyperb…
Let $N, p \geq 5$ be primes such that $N \equiv 1 \bmod p$. We study the rank $r$ of the Hecke algebra that parametrizes modular forms of weight 2 and level $N$ that are Eisenstein modulo $p$. When $r$ is $2$ or $3$, we prove that $r-1$…
The class of gravito-electric, algebraically general, rotating `silent' dust space-times is studied. The main invariant properties are deduced. The number $t_0$ of functionally independent zero-order Riemann invariants satisfies $1\leq…
We investigate in the simplest compact D=4 N=1 Type IIB orientifold models the sigma-model symmetry suggested by the proposed duality of these models to heterotic orbifold vacua. This symmetry is known to be present at the classical level,…
We build the first example of a hyperbolic 6-manifold that admits a perfect circle-valued Morse function, which can be considered as the analogue of a fibration over the circle for manifolds with non-vanishing Euler characteristic. As a…
We discuss analogues of the prime number theorem for a hyperbolic rational map f of degree at least two on the Riemann sphere. More precisely, we provide counting estimates for the number of primitive periodic orbits of f ordered by their…
Lustig gave an infinite product formula for the zeta function of a commutative two-dimensional regular local ring with finite residue field. We extend this to the noncommutative setting with a method based on filtration by an invertible…
We prove that the only global strong solution of the periodic rod equation vanishing in at least one point $(t_0,x_0)$ is the identically zero solution. Such conclusion holds provided the physical parameter $\gamma$ of the model (related to…
This is a continuation of the research in [16]. Let $(\overline{M},g_{-1})$ be a closed geodesic $r_0$-ball in the hyperbolic space $(\mathbb{H}^n,g_{-1})$. Let $m\neq1$ be a positive constant. In this paper, we show that for $n\geq3$,…
In this paper, we show that every invertible subsheaf of the cotangent bundle of a smooth globally $F$-regular threefold of characteristic $p>3$ has Iitaka dimension less than or equal to one.
We present the first example of the Selberg type zeta function for noncompact higher rank locally symmetric spaces. We study certain Selberg type zeta functions and Ruelle type zeta functions attached to the Hilbert modular group of a real…
We consider the Rumin complex associated with a generic rank two distribution on a closed 5-manifold. The Rumin differential in middle degrees gives rise to a self-adjoint differential operator of Heisenberg order two. We study the eta…
In this paper we consider axisymmetric black holes in supergravity and address the general issue of defining a first order description for them. The natural setting where to formulate the problem is the De Donder-Weyl-Hamilton-Jacobi theory…
We apply the nonperturbative functional renormalization group (NP-FRG) in the superfield formalism that we have developed in the preceding paper to study long-standing issues concerning the critical behavior of the random field Ising model.…
We show how the small perturbations of a linear cocycle have a relative rotation number associated with an invariant measure of the base dynamics an with a $2$-dimensional bundle of the finest dominated splitting (provided that some…
We consider the Steklov zeta function $\zeta$ $\Omega$ of a smooth bounded simply connected planar domain $\Omega$ $\subset$ R 2 of perimeter 2$\pi$. We provide a first variation formula for $\zeta$ $\Omega$ under a smooth deformation of…
We consider the renormalization group flow equation for the two-dimensional sigma models with the K\"ahler target space. The first-order formulation allows us to treat perturbations in these models as current-current deformations. We…
We study the motion of an incompressible, inviscid two-dimensional fluid in a rotating frame of reference. There the fluid experiences a Coriolis force, which we assume to be linearly dependent on one of the coordinates. This is a common…
We consider the hyperbolic-parabolic singular perturbation problem for a nondegenerate quasilinear equation of Kirchhoff type with weak dissipation. This means that the dissipative term is multiplied by a coefficient b(t) which tends to 0…
In this paper we continue the study of perturbative renormalizations in an $\mathcal{N}=(0,2)$ supersymmetric model. Previously we analyzed one-loop graphs in the heterotically deformed CP$(N-1)$ models. Now we extend the analysis of the…
The explicit formula for the hyperbolic metric $\lambda_{\alpha,\,\beta,\,\gamma}(z)|dz|$ on the thrice-punctured sphere $\mathbb{P} \backslash \{z_1,\,z_2,\,z_3\}$ with singularities of order $\alpha,\,\beta,\,\gamma \leq 1$ with…