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29 March 2024
 
  » arxiv » math.QA/0010140

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Relations of multiple zeta values and their algebraic expression
Michael E. Hoffman ; Yasuo Ohno ;
Date 13 Oct 2000
Journal J. Algebra 262 (2003), 332-347
Subject Quantum Algebra MSC-class: 16W30 (Primary), 11M06, 16W25 (Secondary) | math.QA
AbstractWe establish a new class of relations among the multiple zeta values zeta(k_1,k_2,...,k_n), which we call the cyclic sum identities. These identities have an elementary proof, and imply the "sum theorem" for multiple zeta values. They also have a succinct statement in terms of "cyclic derivations" as introduced by Rota, Sagan and Stein. In addition, we discuss the expression of other relations of multiple zeta values via the shuffle and "harmonic" products on the underlying vector space H of the noncommutative polynomial ring Q, and also using an action on Q of the Hopf algebra of quasi-symmetric functions.
Source arXiv, math.QA/0010140
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