Dedekind Zeta Motives for Totally Real Fields

Let k be a totally real number field. For every odd n ≥ 3, we construct a Dedekind zeta motive in the category MT(k) of mixed Tate motives over k. By directly calculating its Hodge realisation, we prove that its period is a rational multiple of πn[k:Q]ζ∗ k (1 − n), where ζ∗ k (1 − n) denotes the special value of the Dedekind zeta function of k. We deduce… CONTINUE READING