Meromorphic continuation of Selberg zeta functions with twists having non-expanding cusp monodromy

• Ksenia Fedosova ^[1] ; Anke Pohl ^[2]
  1. [1] University of Freiburg

     University of Freiburg

     Stadtkreis Freiburg im Breisgau, Alemania

     
  2. [2] University of Bremen

     University of Bremen

     Kreisfreie Stadt Bremen, Alemania

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 1, 2020
• Idioma: inglés
• DOI: 10.1007/s00029-019-0534-3
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• Resumen

  • We initiate the study of Selberg zeta functions ZΓ,χ for geometrically finite Fuchsian groups Γ and finite-dimensional representations χ with non-expanding cusp monodromy. We show that for all choices of (Γ,χ), the Selberg zeta function ZΓ,χ converges on some half-plane in C. In addition, under the assumption that Γ admits a strict transfer operator approach, we show that ZΓ,χ extends meromorphically to all of C.