Mollified moments of cubic Dirichlet \(L\)-functions over the Eisenstein field (Q6146382)

In the paper under review, the authors consider a particular family \(\mathcal{F}\) of primitive cubic Dirichlet characters \(\chi\) over the Eisenstein field and they show that assuming the generalized Riemann hypothesis (GRH) there is a small positive proportion of non-vanishing \(L(1/2, \chi)\). The proof relies on sharp upper bounds for the first mollified moments of \(L\)-functions and follows a similar approach of the paper by \textit{C. David} et al. [Forum Math. Sigma 9, Paper No. e69, 58 p. (2021; Zbl 1495.11099)].