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Evaluation of the zeta functions of totally real number fields and its application. (English) Zbl 1439.11282

Summary: In this paper, we are interested in the evaluation of special values of the Dedekind zeta function of a totally real number field. In particular, we revisit Siegel method for values of the zeta function of a totally real number field at negative odd integers and explain how this method is applied to the case of non-normal totally real number field. As one of its applications, we give divisibility property for the values in the special case.

MSC:

11R42 Zeta functions and \(L\)-functions of number fields
11R16 Cubic and quartic extensions
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References:

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