Related papers: Eisenstein series and Scattering matrices
We develop a geometric scattering theory for a geometrically finite group acting on (a vector bundle over) a symmetric space of negative curvature. In particular, we obtain the meromorphic continuation of Eisenstein series and scattering…
In this paper we consider discrete groups in ${\rm PGL}_d(\mathbb{R})$ acting convex co-compactly on a properly convex domain in real projective space. For such groups, we establish necessary and sufficient conditions for the group to be…
We prove that the modular symbols appropriately normalized and ordered have an asymptotical normal distribution for all cocompact subgroups of SL_2(R). We introduce hyperbolic Eisenstein series in order to calculate the moments of the…
We study a notion of convex cocompactness for discrete subgroups of the projective general linear group acting (not necessarily irreducibly) on real projective space, and give various characterizations. A convex cocompact group in this…
In this work we give an explicit formula for the Fourier coefficients of Eisenstein series corresponding to certain arithmetic lattices acting on hyperbolic n+1-space. As a consequence we obtain results on location of all poles of these…
Eisenstein series are ubiquitous in the theory of automorphic forms. The traditional proofs of the meromorphic continuation of Eisenstein series, due to Selberg and Langlands, start with cuspidal Eisenstein series as a special case, and…
Let $G$ be an infinite-dimensional representation-theoretic Kac--Moody group associated to a nonsingular symmetrizable generalized Cartan matrix. We consider Eisenstein series on $G$ induced from unramified cusp forms on finite-dimensional…
The purpose of this of this paper is to develop the theory of Eisenstein series in the framework of geometric Langlands correspondence. Our construction is based on the study of certain relative compactification of the moduli stack of…
For convex co-compact hyperbolic manifolds $\Gamma\backslash \mathbb{H}^{n+1}$ for which the dimension of the limit set satisfies $\delta_\Gamma< n/2$, we show that the high-frequency Eisenstein series associated to a point $\xi$ "at…
Quantum graphs can be extended to scattering systems when they are connected by leads to infinity. It is shown that for certain extensions, the scattering matrices of isospectral graphs are conjugate to each other and their poles…
We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems involving systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…
We consider an inverse problem associated with some 2-dimensional non-compact surfaces with conical singularities, cusps and regular ends. Our motivating example is a Riemann surface $\mathcal M = \Gamma\backslash{\bf H}^2$ associated with…
We derive a formula for the regularized trace of operators with compact spectrum which act on the space of square integrable functions on the quotient of a semisimple Liegroup of real rank one by a convex-cocompact subgroup. The sum of…
At first a type of Eisenstein series is defined as distributions giving nearly-holomorphic automorphic forms on a totally real field, with different expressions (integral, summation) ; then these are shown to satisfied the expected…
On convex co-compact hyperbolic surfaces with Hausdorff dimension of the limit set less than 1/2, we investigate high energy behaviour of Eisenstein Series. Eisenstein Series are non-L^2 eigenfunctions of the hyperbolic Laplacian which…
Let $\Gamma$ be a Fuchsian group of the first kind acting on the hyperbolic upper half plane $\mathbb H$, and let $M = \Gamma \backslash \mathbb H$ be the associated finite volume hyperbolic Riemann surface. If $\gamma$ is parabolic, there…
We consider the matrix representation of the Eisenstein numbers and in this context we discuss the theory of the Pseudo Hyperbolic Functions. We develop a geometrical interpretation and show the usefulness of the method in Physical problems…
The family hyperbolic metric for the plumbing variety $\{zw=t\}$ and the non holomorphic Eisenstein series $E(\zeta;2)$ are combined to provide an explicit expansion for the hyperbolic metrics for degenerating families of Riemann surfaces.…
On the basis of the explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equal deficiency indices, we derive a new representation for the…
In this paper we consider scattering theory on manifolds with special cusp-like metric singularities of warped product type g=dx^2 + x^(-2a)h, where a>0. These metrics form a natural subset in the class of metrics with warped product…