Vanishing of Dirichlet L-functions at the central point over function fields

@article{Donepudi2020VanishingOD,
  title={Vanishing of Dirichlet L-functions at the central point over function fields},
  author={Ravi Donepudi and Wanlin Li},
  journal={Rocky Mountain Journal of Mathematics},
  year={2020}
}
We give a geometric criterion for Dirichlet L-functions associated to cyclic characters over the rational function field Fq(t) to vanish at the central point s = 1/2. The idea is based on the observation that vanishing at the central point can be interpreted as the existence of a map from the projective curve associated to the character to some abelian variety over Fq. Using this geometric criterion, we obtain a lower bound on the number of cubic characters over Fq(t) whose L-functions vanish… 

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