Class Number One Criterion for Some Non-Normal Totally Real Cubic Fields

Abstract

Let {K m } m≥4 be the family of non-normal totally real cubic number fields defined by the irreducible cubic polynomial f m (x) = x 3 − mx 2 − (m + 1)x − 1, where m is an integer with m ≥ 4. In this paper, we will give a class number one criterion for K m .