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.
Contents
Full-Text PDF