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

開催日時
2022/12/09 金 13:30 - 14:30
場所
3号館152号室
講演者
戸次鵬人
講演者所属
慶應義塾大学
概要

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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