Czechoslovak Mathematical Journal, Vol. 70, No. 4, pp. 1167-1178, 2020
Exponent of class group of certain imaginary quadratic fields
Kalyan Chakraborty, Azizul Hoque
Received June 29, 2019. Published online September 15, 2020.
Abstract: Let $n>1$ be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form $\mathbb{Q} \bigl(\sqrt{x^2-2y^n} \bigr)$ whose ideal class group has an element of order $n$. This family gives a counterexample to a conjecture by H. Wada (1970) on the structure of ideal class groups.
Keywords: quadratic field; discriminant; class group; Wada's conjecture
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Affiliations: Kalyan Chakraborty, Azizul Hoque (corresponding author), Harish-Chandra Research Institute, Homi Bhabha National Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India, e-mail: kalyan@hri.res.in, ahoque.ms@gmail.com
