Non-Vanishing of High Derivatives of Dirichlet L-Functions at the Central Point Original Research Article

Using the mollification method, we show that, for large q, at least 2/3−O(k−2) of the set {Λ(k)(χ, 1/2)} is non-zero, where Λ(χ, s) is the complete Dirichlet L-function and χ runs over all even primitive characters modulo q.