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1. Upper Bounds on the Number of Resonances for Non-compact Riemann Surfaces

Author

Laurent Guillopé

Subjects
Pure mathematics, Polynomial, Riemann surface, Mathematical analysis, Function (mathematics), Type (model theory), Riemann Xi function, symbols.namesake, symbols, Laplace operator, Analysis, Resolvent, Meromorphic function, Mathematics
Abstract

Let X be a Riemannian surface of finite geometric type and with hyperbolic ends. The resolvent (ΔX−s(1−s))−1, Re s > 1 of the Laplacian on X extends to a meromorphic family of operators on C and its poles are called resonances. We prove an optimal polynomial bound for their counting function.

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