Combinatorial aspects of multiple zeta values

Title: Combinatorial aspects of multiple zeta values
Creator: Borwein, Jonathan M.; Bradley, David M.; Broadhurst, David J.; Lisoněk, Petr
Relation: Electronic Journal of Combinatorics Vol. 5
Relation: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v5i1r38
Publisher: Electronic Journal of Combinatorics
Resource Type: journal article
Date: 1998
Description: Multiple zeta values (MZVs, also called Euler sums or multiple harmonic series) are nested generalizations of the classical Riemann zeta function evaluated at integer values. The fact that an integral representation of MZVs obeys a shuffle product rule allows the possibility of a combinatorial approach to them. Using this approach we prove a longstanding conjecture of Don Zagier about MZVs with certain repeated arguments. We also prove a similar cyclic sum identity. Finally, we present extensive computational evidence supporting an infinite family of conjectured MZV identities that simultaneously generalize the Zagier identity.
Subject: Zagier identity; multiple zeta values; MZVs; Euler sums
Identifier: http://hdl.handle.net/1959.13/940456
Identifier: uon:13016
Identifier: ISSN:1077-8926
Language: eng
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