Communications of the
Korean Mathematical Society CKMS

Using p-adic class number formula, we derive a congruence relation for class numbers of the simplest cubic fields which can be considered as a cubic analogue of Ankeny-Artin-Chowla's theorem. Furthermore, we give an elementary proof for an upper bound for the class numbers of the simplest cubic fields.

Keywords: simplest cubic field, class number

MSC numbers: 11R16, 11R29