Divisor of the Selberg zeta function for kleinian groups

Peter A. Perry

Displaying similar documents to “Divisor of the Selberg zeta function for kleinian groups”

The Lax-Phillips infinitesimal generator and the scattering matrix for automorphic functions

Yoichi Uetake (2007)

Annales Polonici Mathematici

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We study the infinitesimal generator of the Lax-Phillips semigroup of the automorphic scattering system defined on the Poincaré upper half-plane for SL₂(ℤ). We show that its spectrum consists only of the poles of the resolvent of the generator, and coincides with the poles of the scattering matrix, counted with multiplicities. Using this we construct an operator whose eigenvalues, counted with algebraic multiplicities (i.e. dimensions of generalized eigenspaces), are precisely the non-trivial...

On poles of scattering matrices for several convex bodies

Mitsuru Ikawa (1990)

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On zeta function and scattering poles for several convex bodies

Mitsuru Ikawa (1994)

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Poisson formulæ for resonances.

Maciej Zworski (1996-1997)

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Sharp bounds for the number of the scattering poles

Georgi Vodev (1992)

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Distribution of resonances for convex co-compact hyperbolic surfaces

Maciej Zworski (1997)

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A scattering theory for automorphic functions

P. D. Lax, R. S. Phillips (1973-1974)

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Scattering and resolvent on geometrically finite hyperbolic manifolds with rational cusps

Colin Guillarmou (2005-2006)

Séminaire Équations aux dérivées partielles

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These notes summarize the papers [, ] on the analysis of resolvent, Eisenstein series and scattering operator for geometrically finite hyperbolic quotients with rational non-maximal rank cusps. They complete somehow the talk given at the PDE seminar of Ecole Polytechnique in october 2005.