Quadratic class numbers divisible by 3 (Q2479920)

It follows from a result of \textit{K. Soundararajan} [J. Lond. Math. Soc. (2) 61, No. 3, 681--690 (2000; Zbl 1018.11054)] that the number of square-free numbers \(0<d\leq x\) for which the class-number of the field \(\mathbb Q(\sqrt{-d})\) is divisible by \(3\) is for every \(\varepsilon>0\) greater than \(B(\varepsilon)x^{7/8-\varepsilon}\) (with positive \(B(\varepsilon)\)), and his method has been utilized by \textit{D. Byeon} and \textit{E. Koh} [Manuscr. Math. 111, 261--263 (2003; Zbl 1125.11060)] to get the same assertion for real quadratic fields. In the reviewed paper an improvement of Soundararajan's approach is presented, which in both cases leads to the replacement of \(7/8\) by \(9/10\).