Nagoya Mathematical Journal

Symmetry on linear relations for multiple zeta values

Kentaro Ihara and Hiroyuki Ochiai

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We find a symmetry for the reflection groups in the double shuffle space of depth three. The space was introduced by Ihara, Kaneko and Zagier and consists of polynomials in three variables satisfying certain identities which are connected with the double shuffle relations for multiple zeta values. Goncharov has defined a space essentially equivalent to the double shuffle space and has calculated the dimension. In this paper we relate the structure among multiple zeta values of depth three with the invariant theory for the reflection groups and discuss the dimension of the double shuffle space in this view point.

Article information

Nagoya Math. J., Volume 189 (2008), 49-62.

First available in Project Euclid: 10 March 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11M41: Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}
Secondary: 11M06: $\zeta (s)$ and $L(s, \chi)$ 40B05: Multiple sequences and series (should also be assigned at least one other classification number in this section)


Ihara, Kentaro; Ochiai, Hiroyuki. Symmetry on linear relations for multiple zeta values. Nagoya Math. J. 189 (2008), 49--62.

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