Finite multiple zeta values associated with 2-colored rooted trees

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1 Citation (Scopus)

Abstract

We define finite multiple zeta values (FMZVs) associated with some combinatorial objects, which we call 2-colored rooted trees, and prove that FMZVs associated with 2-colored rooted trees satisfying certain mild assumptions can be written explicitly as Z-linear combinations of the usual FMZVs. Our result can be regarded as a generalization of Kamano's recent work on finite Mordell–Tornheim multiple zeta values. As an application, we will give a new proof of the shuffle relation of FMZVs, which was first proved by Kaneko and Zagier.

Original languageEnglish
Pages (from-to)99-116
Number of pages18
JournalJournal of Number Theory
Volume181
DOIs
Publication statusPublished - 2017 Dec
Externally publishedYes

Keywords

  • Finite multiple zeta values
  • Trees

ASJC Scopus subject areas

  • Algebra and Number Theory

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