Class number one criterion for some non-normal totally real cubic fields. (English) Zbl 1282.11149

Lee, Jun Ho

Taiwanese J. Math. 17, No. 3, 981-989 (2013).

Summary: 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 \(K_m\).

MSC:

11R42	Zeta functions and \(L\)-functions of number fields
11R16	Cubic and quartic extensions
11R29	Class numbers, class groups, discriminants

Keywords:

cubic fields; class number; zeta function