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Let  L ( E /ℚ,  s ) be the  L ‐function of an elliptic curve  E  defined over the rational field ℚ. We examine the vanishing and non‐vanishing of the central values  L ( E , 1, χ) of the twisted  L ‐function as χ ranges over Dirichlet characters of a given order.

Vanishing and non‐vanishing Dirichlet twists of L ‐functions of elliptic curves