Negative moments of the Riemann zeta-function (Q6186151)

In the paper under review, the authors obtain bounds for the negative moments of the Riemann zeta-function, which is defined for \(k>0\) and \(\alpha>0\) by \[ I_{-k}(\alpha, T)=\frac{1}{T}\int_0^T\zeta\Big(\frac{1}{2}+\alpha+it\Big)^{-2k}\,dt. \] All the results are conditional, under assuming the Riemann hypothesis, and described for various ranges of variables. As an application, they study averages of the generalized Möbius function \(\mu_k(n)\) denoting the \(n\)-th Dirichlet coefficient of \(\zeta(s)^{-k}\).