Riemann’s Theorem on the Singularities of Θ

  • Raghavan Narasimhan
Part of the Lectures in Mathematics ETH Zürich book series (LM)


Riemann’s singularity theorem expresses the order of vanishing of the ϑ-function at a point ζ Θ in terms of dim |D|, where D ≥ 0 is a divisor of degree g − 1 with ζ − κ = A(D). Riemann proves this by relating this order to the vanishing of ϑ on sets of the form W rW r − ζ (Über das Verschwinden der Theta-Functionen).


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Copyright information

© Springer Basel AG 1992

Authors and Affiliations

  • Raghavan Narasimhan
    • 1
  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA

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