• search hit 1 of 1
Back to Result List

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.

Export metadata

Additional Services

Search Google Scholar Statistics
Metadaten
Author details:Li Guo, Sylvie PaychaORCiDGND, Bin Zhang
DOI:https://doi.org/10.1016/j.aim.2013.10.022
ISSN:0001-8708
ISSN:1090-2082
Title of parent work (English):Advances in mathematics
Publisher:Elsevier
Place of publishing:San Diego
Publication type:Article
Language:English
Year of first publication:2014
Publication 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
Volume:252
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
Accept ✔
This website uses technically necessary session cookies. By continuing to use the website, you agree to this. You can find our privacy policy here.