On the number of real quadratic fields with class number divisible by 3

Chakraborty, K.; Murty, M.

doi:10.1090/S0002-9939-02-06603-0

On the number of real quadratic fields with class number divisible by 3
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by K. Chakraborty and M. Ram Murty PDF

Proc. Amer. Math. Soc. 131 (2003), 41-44 Request permission

Abstract:

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.

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