The distribution of values of \(\frac{L^\prime}{L}(1 / 2 + \epsilon, \chi_D)\) (Q2162838)

Let \(\chi_{D}(n)\) be the Kronecker symbol and \(0<\varepsilon<1/2\). The authors write: ``We determine the limiting distribution of the family of values \(\frac{L'}{L}(1/2+\varepsilon,\chi_{D})\) as \(D\) varies over fundamental discriminants\dots Moreover, we also establish an upper bound for the rate of convergence of this family to its limiting distribution.'' This result strengthens a theorem of \textit{M. Mourtada} and \textit{V. K. Murty} [Mosc. Math. J. 15, No. 3, 497--509 (2015; Zbl 1382.11058)]. For \(N\in\mathbb{N}\), let \(F(N)\) be the set of fundamental discriminants in the interval \([-N, N]\) and let \[ m(N):=\min\left\{\left|\frac{L'}{L}(1/2+\varepsilon,\chi_{D})\right|: D\in F(N)\right\}; \] as a consequence of their results, the authors obtain the upper bound \[ m(N)<< \left(\frac{\log\log n}{\log n}\right)^{1/2+\varepsilon}\ \text{ as }N\rightarrow\infty. \]