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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:Li Guo, Sylvie PaychaORCiDGND, Bin Zhang
ISSN:0001-8708 (print)
ISSN:1090-2082 (online)
Parent Title (English):Advances in mathematics
Place of publication:San Diego
Document Type:Article
Year of first Publication:2014
Year of Completion: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
First Page:343
Last Page:381
Funder:NSF [DMS 1001855]; NSFC [11071176, 11221101]
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Peer Review:Referiert