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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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