The conical zeta values are the real numbers defined by certain multiple sums over convex 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 is known about the conical zeta values for non-rational cones. In this talk, 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. A key tool we use is a generalization of the classical Hecke integral formula which expresses the values of the zeta functions of real quadratic fields as an integral of the Eisenstein series along the closed geodesics on the modular curve.
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