A theta function for hyperbolic surfaces with cusps

1994/07/22 by Ulrich Bunke, Bunke, Ulrich, Martin Olbrich +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #dg-ga #math.DG

paper · pdf · doi:10.48550/arxiv.dg-ga/9407014

16 pages, Latex, reportSFB288-112

arxiv created 1994/07/22 · openalex publication_date 1994/07/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Theta and zeta functions for odd-dimensional locally symmetric spaces of rank one

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