Prefer a chat interface with context about you and your work?
On the unit groups and the ideal class groups of certain cubic number fields
Let f(x)=x3+3x+a3(a∈Z) be a cubic polynomial and θ be the real root of f(x). We consider the unit group of Q(θ). We show that η=1−a2−αθ is a fundamental unit of Q(θ) under certain conditions. And we consider the 3-class group of Q(θ).