Riemann’s Theorem on the Singularities of Θ
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 r − W r − ζ (Über das Verschwinden der Theta-Functionen).
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