Result: Relations of multiple zeta values and their algebraic expression: Relations of multiple zeta values and their algebraic expression.
Title:
Relations of multiple zeta values and their algebraic expression: Relations of multiple zeta values and their algebraic expression.
Authors:
Source:
Journal of Algebra. 262:332-347
Publication Status:
Preprint
Publisher Information:
Elsevier BV, 2003.
Publication Year:
2003
Subject Terms:
Cyclic derivation, Symmetric functions and generalizations, Algebra and Number Theory, cyclic derivation, 16W30 (Primary), 11M06, 16W25 (Secondary), quasi-symmetric functions, multiple zeta values, Multiple zeta values, 01 natural sciences, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Quasi-symmetric functions, Multiple Dirichlet series and zeta functions and multizeta values, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), 0101 mathematics
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
0021-8693
DOI:
10.1016/s0021-8693(03)00016-4
DOI:
10.48550/arxiv.math/0010140
Access URL:
http://arxiv.org/abs/math/0010140
https://zbmath.org/1917898
https://doi.org/10.1016/s0021-8693(03)00016-4
https://www.sciencedirect.com/science/article/pii/S0021869303000164
https://www.sciencedirect.com/science/article/abs/pii/S0021869303000164
https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_3124926
https://tohoku.pure.elsevier.com/en/publications/relations-of-multiple-zeta-values-and-their-algebraic-expression
https://zbmath.org/1917898
https://doi.org/10.1016/s0021-8693(03)00016-4
https://www.sciencedirect.com/science/article/pii/S0021869303000164
https://www.sciencedirect.com/science/article/abs/pii/S0021869303000164
https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_3124926
https://tohoku.pure.elsevier.com/en/publications/relations-of-multiple-zeta-values-and-their-algebraic-expression
Rights:
Elsevier Non-Commercial
arXiv Non-Exclusive Distribution
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....4d4ad818fade2d906a52a4850da7a38c
Database:
OpenAIRE
Further Information
We establish a new class of relations among the multiple zeta values ��(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.
14 pages AMS-TeX