Conical zeta values and their double subdivision relations

Li Guo, Sylvie Paycha, Bin Zhang

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)343-381
Number of pages39
JournalAdvances in Mathematics
StatePublished - Feb 15 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


  • Conical zeta values
  • Convex cones
  • Decorated cones
  • Fractions with linear poles
  • Multiple zeta values
  • Quasi-shuffles
  • Shintani zeta values
  • Shuffles
  • Smooth cones
  • Subdivisions

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