Abstract
Let $m_1$ and $m_2$ be distinct square-free integers. We show that there exist infinitely many pairs of quadratic fields $\mathbb{Q}(\sqrt{m_1D})$ and $\mathbb{Q}(\sqrt{m_2D})$ whose class numbers are both divisible by $3$ under the splitting conditions of prime numbers. This improves results of T. Komatsu and the author.
Citation
Akiko Ito. "On the $3$-divisibility of class numbers of pairs of quadratic fields with splitting conditions." Funct. Approx. Comment. Math. 60 (1) 61 - 76, March 2019. https://doi.org/10.7169/facm/1688