CLASS NUMBER ONE CRITERION FOR SOME NON-NORMAL TOTALLY REAL CUBIC FIELDS

Abstract

Let ${\{K_m\}_{m\geq 4}}$ 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 $m\geq 4$. In this paper, we will give a class number one criterion for $K_m$.