A theta function for hyperbolic surfaces with cusps
classification
dg-ga
math.DG
keywords
cuspsfunctionsingularitiesthetacontinuationdefinedeterminantdiscuss
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For a Riemann surface with cusps we define a theta function using the eigenvalues of the Laplacian and the singularities of the scattering determinant. We provide its meromorphic continuation and discuss its singularities.
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