飯塚 義睦

Let l be the prime 3, 5 or 7, and let m(1), m(2), n(1) and n(2) be non-zero rational numbers. We construct an infinite family of pairs of distinct quadratic fields Q(root m(1)D + n(1)) and Q(root m(2)D + n(2)) with D is an element of Q such that both class numbers are divisible by l, using rational points on an elliptic curve with positive Mordell-Weil rank to parametrize such quadratic fields.

We construct an infinite family of pairs of imaginary quadratic fields Q(root D) and Q(root D + 1) with D is an element of Z whose class numbers are both divisible by 3. (C) 2017 Elsevier Inc. All rights reserved.

Let l be the prime 3, 5 or 7 and let m be a nonzero integer. We give a method for constructing an infinite family of pairs of quadratic fields Q(root D) and Q(root mD) with both class numbers divisible by l. Such quadratic fields are parametrized by rational points on a specified elliptic curve.