, Volume 124, Issue 4, pp 551-560
Date: 05 Oct 2007

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

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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 .

This work was supported by grant No.R01-2006-000-11176-0 from the Basic Research Program of KOSEF.