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Conical zeta values and their double subdivision relations

  • We introduce the concept of a conical zeta value as a geometric generalization of a multiple zeta value in the context of convex cones. The quasi-shuffle and shuffle relations of multiple zeta values are generalized to open cone subdivision and closed cone subdivision relations respectively for conical zeta values. In order to achieve the closed cone subdivision relation, we also interpret linear relations among fractions as subdivisions of decorated closed cones. As a generalization of the double shuffle relation of multiple zeta values, we give the double subdivision relation of conical zeta values and formulate the extended double subdivision relation conjecture for conical zeta values.

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Author details:Li Guo, Sylvie PaychaORCiDGND, Bin Zhang
Title of parent work (English):Advances in mathematics
Place of publishing:San Diego
Publication type:Article
Year of first publication:2014
Completion year:2014
Release date:2017/03/27
Tag:Conical zeta values; Convex cones; Decorated cones; Fractions with linear poles; Multiple zeta values; Quasi-shuffles; Shintani zeta values; Shuffles; Smooth cones; Subdivisions
Number of pages:39
First page:343
Last Page:381
Funding institution:NSF [DMS 1001855]; NSFC [11071176, 11221101]
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Peer review:Referiert