For quadratic twists of elliptic curves over Q, the Taylor coefficients of their L-functions at the central point are non-vanishing for large discriminants under GRH, with an unconditional lower bound on the number of non-vanishing ones derived from moments of central values.
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On the coefficients of the Taylor expansion of $L$-functions of elliptic curves
For quadratic twists of elliptic curves over Q, the Taylor coefficients of their L-functions at the central point are non-vanishing for large discriminants under GRH, with an unconditional lower bound on the number of non-vanishing ones derived from moments of central values.