Relations of multiple zeta values and their algebraic expression
Copyright policy )Relations of multiple zeta values and their algebraic expression
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
- United States Naval Academy United States
- Kindai University Japan
- U.S. NAVAL ACADEMY
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, 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)
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, 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)
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