English

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

Mathematical Physics 2012-03-12 v2 math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.1111.6198,
  title  = {The trace formula for a point scatterer on a hyperbolic surface with one cusp},
  author = {Henrik Ueberschaer},
  journal= {arXiv preprint arXiv:1111.6198},
  year   = {2012}
}

Comments

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

R2 v1 2026-06-21T19:41:59.566Z