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We compute the divisor of Selberg's zeta function for convex co-compact, torsion-free discrete groups ? acting on a real hyperbolic space of dimension n + 1. The divisor is determined by the eigenvalues and scattering poles of the Laplacian on X = ?nH n+1 together with the Euler characteristic of X compactiied to a manifold with boundary. If n is even, the… (More)

F or convex co-compact hyperbolic manifolds of even dimension n + 1 , w e derive a P oisson-type formula for scattering resonances which m a y be regarded as a version of Selberg's trace formula for these manifolds. Using techniques of Guillop e and Zworski we easily obtain an O ; R n+1 lower bound for the counting functionfor scattering resonances together… (More)

- PETER A. PERRY
- 2000

W e compute the leading asymptotics of the counting function for closed geodesics on a convex co-compact hyperbolic manifold in terms of spectral data and scattering resonances for the Laplacian. Our result extends classical results of Selberg for compact and nite-volume surfaces to this class of innnite-volume h yperbolic manifolds. 1. Introduction… (More)

A Selberg zeta function is attached to the three-dimensional BTZ black hole, and a trace formula is developed for a general class of test functions. The trace formula differs from those of more standard use in physics in that the black hole has a fundamental domain of infinite hyperbolic volume. Various thermodynamic quantities associated with the black… (More)

- Peter A Perry
- 1995

Suppose that ? 1 and ? 2 are geometrically nite, convex co-compact, discrete groups of isometries of real hyperbolic space H 3 whose domains of discontinuity are diieomorphic. We show that if the respective scattering matrices S 1 (s) and S 2 (s) diier from each other by a trace-class perturbation on the unitary axis Re(s) = 1, then ? 1 and ? 2 are… (More)

- T. Kappeler, P. Perry, M. Shubin, P. Topalov
- 2006

We investigate the relation between the Korteweg-de Vries and modified Korteweg-de Vries equations (KdV and mKdV), and find a new algebro-analytic mechanism, similar to the Lax L-A pair, which involves a family of first-order operators Q λ depending on a spectral parameter λ, instead of the third-order operator A. In our framework, any generalized… (More)

The need for policies to control calls is justified by the changing face of communications. It is argued that call control requires distinctive capabilities in a policy system. A spe-cialised policy language called APPEL (ACCENT Project Policy Environment/Language) has therefore been developed for this purpose. However the policy language is cleanly… (More)

For a large class of two body potentials, we solve two of the main problems in the spectral analysis of multiparticle quantum Hamiltonians: explicitly, we prove that the point spectrum lies in a closed countable set (and describe that set in terms of the eigenvalues of Hamiltonians of subsystems) and that there is no singular continuous spectrum. We… (More)

We consider the problem of enumerating permutations in the symmetric group on n elements which avoid a given set of consecutive pattern S, and in particular computing asymptotics as n tends to infinity. We develop a general method which solves this enumeration problem using the spectral theory of integral operators on L 2 ([0, 1] m), where the patterns in S… (More)

- David Borthwick, Chris Judge, Peter A. Perry, DAVID BORTHWICK
- 2001

We construct a determinant of the Laplacian for infinite-area surfaces which are hyperbolic near infinity and without cusps. In the case of a convex co-compact hyperbolic metric, the determinant can be related to the Selberg zeta function and thus shown to be an entire function of order two with zeros at the eigenvalues and resonances of the Laplacian. In… (More)