Divisibility of class numbers of certain families of quadratic fields

Abstract

We construct some families of quadratic fields whose class numbers are divisible by $3.$ The main tools used are a trinomial introduced by Kishi and a parametrization of Kishi and Miyake of a family of quadratic fields whose class numbers are divisible by $3.$ At the end we compute class number of these fields for some small values and verify our results.

13 Pages, accepted for publication in Journal of the Ramanujan Mathematical Society, 2017