The trace formula for a point scatterer on a hyperbolic surface with one cusp

Details The trace formula for a point scatterer on a hyperbolic surface with one cusp The trace formula for a point scatterer on a hyperbolic surface with one cusp

2011-11-26

arxiv.org/abs/1111.6198v2

Physics

Mathematical Physics

34 pages. minor changes, added some details and minor changes of notation. arXiv admin note: text overlap with arXiv:1002.2930

Scientific paper

We prove an exact trace formula for the Laplacian with a delta potential -
also known as a point scatterer - on a non-compact hyperbolic surface of finite
volume with one cusp. Our formula is an analogue of the Selberg trace formula.
We express the difference of perturbed and unperturbed trace as a smooth term
plus a sum over combinations of diffractive orbits.

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