On the conical zeta values and the Dedekind zeta values for totally real fields

The conical zeta values are the real numbers defined by certain multiple sums over cones which can be seen as a generalization of the multiple zeta values. If the cones are rational, it is known that such conical zeta values are related to the cyclotomic multiple zeta values. On the other hand, it seems that little was known about the conical zeta values for non-rational cones. In this talk, I will discuss the case where the cones are irrational and algebraic. More precisely, I would like to present a relation between the conical zeta values associated with certain algebraic cones and the values of the partial zeta functions of totally real fields.