# Journal of the Ramanujan Mathematical Society

Volume 34, Issue 4, December 2019 pp. 389–392.

A short note on the divisibility of class numbers of real quadratic fields

**Authors**:
Jaitra Chattopadhyay

**Author institution:**Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhunsi, Allahabad 211 019, India

**Summary: **
For any integer l ≥ 1, let p1, p2, ..., p l+2 be
distinct prime numbers ≥ 5. For all real numbers X > 1, we
let N 3,l (X) denote the number of real quadratic fields K
whose absolute discriminant dK ≤ X and dK is divisible by
(p1 ... pl+2) together with the class number hK of K
divisible by 2l · 3. Then, in this short note, by
following the method in [3], we prove that
N3,l (X) > > X 7/8 for all large enough X's.

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