In this talk, we present asymptotic formulas for the first and second moments of central L-derivative values for holomorphic weight-2k Hecke eigencusp forms in a basis B2k for large odd k, with arbitrary power saving. Also, we will illustrate the use of mollifiers to obtain that there are positive proportion of forms in B2k with non-vanishing central L-derivative value, as k tends to infinity, regardless of k being odd or even.