单尖点双曲曲面上点散射体的迹公式
The trace formula for a point scatterer on a hyperbolic surface with one cusp
摘要：
我们证明了一个精确的跟踪公式的拉普拉斯与δ势-也被称为一个点散射体-在一个非紧双曲曲面的有限体积与一个尖点。我们的公式是Selberg迹公式的一个类似物。我们将扰动迹线与未扰动迹线之差表示为光滑项加上衍射轨道组合的和。
英文摘要：
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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