Evaluation of the Dedekind zeta functions of some non-normal totally real cubic fields at negative odd integers

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 apply Siegel's formula for the values of the zeta function of a totally real algebraic number field at negative odd integers to K-m, and compute the values of the Dedekind zeta function of K-m.