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

Conical zeta values are a generalization of multiple zeta values which are defined by certain multiple sums over convex cones. We present a relation between the values of the Dedekind zeta functions for totally real fields and the conical zeta values for certain algebraic cones. More precisely, we show that the values of the partial zeta functions for totally real fields can be expressed as rational linear combinations of the conical zeta values associated with certain algebraic cones up to the square root of the discriminant.