Abstract
Let $N_+(X)$ denote the number of distinct real quadratic fields $\mathbb{Q}(\sqrt{d})$ with $d\leq X$ for which $3|h(\mathbb{Q}(\sqrt{d}))$. Define $N_-(X)$ similarly for $\mathbb{Q}(\sqrt{-d})$. It is shown that $N_+(X), N_-(X)\gg X^{9/10-\varepsilon}$ for any $\varepsilon>0$. This improves results of Byeon and Koh [2] and of Soundararajan [7], which had exponent $7/8-\varepsilon$.
Citation
D. Rodger Heath-Brown. "Quadratic Class Numbers Divisible by 3." Funct. Approx. Comment. Math. 37 (1) 203 - 211, January 2007. https://doi.org/10.7169/facm/1229618751
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