On the number of real quadratic fields with class number divisible by 3
Kalyan Sekhar Chakraborty, M. Ram Murty · Proceedings of the American Mathematical Society · 2002
We find a lower bound for the number of real quadratic fields whose class groups have an element of order $3$. More precisely, we establish that the number of real quadratic fields whose absolute discriminant is $\leq x$ and whose class group has an element of order $3$ is $\gg x^{\frac {5}{6}}$ improving the existing best known bound $\gg x^{\frac {1}{6}}$ of R. Murty.