Chantal David, Jack Fearnley, and Hershey Kivilevsky. On the vanishing of twisted L-functions of elliptic curves. [David's Home Page].
This paper considers the central vanishing of an elliptic curve twisted by a complex Dirichlet character of small order. One might think such L-series never vanish. This paper has very nice theoretical number theory results, numerical results, and heuristics inspired by random matrix theory.
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