Algebraic Aspects of Multiple Zeta Values

DOI10.1007/0-387-24981-8_4zbMath1170.11324arXivmath/0309425OpenAlexW2150017677MaRDI QIDQ5192404

Michael E. Hoffman

Publication date: 5 August 2009

Published in: Zeta Functions, Topology and Quantum Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0309425

zbMATH Keywords

Hopf algebramultiple zeta valuesshuffle productquasi-symmetric functions

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Derivations, actions of Lie algebras (16W25) Associative rings and algebras arising under various constructions (16S99)

Related Items

Duality and (\(q\)-)multiple zeta values, On the reduction of generalized polylogarithms to \(\mathrm{Li}_n\) and \(\mathrm{Li}_{2,2}\) and on the evaluation thereof, Bowman-Bradley type theorem for finite multiple zeta values, A family of super congruences involving multiple harmonic sums, Logarithmic integrals, zeta values, and tiered binomial coefficients, The multiple zeta value data mine, Shuffle products for multiple zeta values and partial fraction decompositions of zeta-functions of root systems, Mod \(p\) structure of alternating and non-alternating multiple harmonic sums, Renormalization of multiple zeta values, Renewal sequences and record chains related to multiple zeta sums, A weighted sum formula for alternating multiple zeta-star values, New properties of multiple harmonic sums modulo 𝑝 and 𝑝-analogues of Leshchiner’s series, A generating function for sums of multiple zeta values and its applications, Sum Relations for Multiple Zeta Values, Hopf Algebras and Transcendental Numbers, Noncommutative algebra, multiple harmonic sums and applications in discrete probability, Generalized Shuffles Related to Nijenhuis andTD-Algebras, An algebraic study of multivariable integration and linear substitution, Harmonic Sums, Polylogarithms,Special Numbers, and Their Generalizations, UNFOLDING THE DOUBLE SHUFFLE STRUCTURE OF -MULTIPLE ZETA VALUES, On Euler's decomposition formula for \(q\)MZVs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Lie elements and an algebra associated with shuffles
• Combinatorial aspects of multiple zeta values
• A cyclic derivative in noncommutative algebra
• Multiple harmonic series
• A natural ring basis for the shuffle algebra and an application to group schemes
• A generalization of the duality and sum formulas on the multiple zeta values
• Kontsevich's integral for the Homfly polynomial and relations between values of multiple zeta functions
• The algebra of multiple harmonic series
• Evaluations of \(k\)-fold Euler/Zagier sums: a compendium of results for arbitrary \(k\)
• Evaluation of triple Euler sums
• The algebra and combinatorics of shuffles and multiple zeta values
• Noncommutative symmetric functions
• Multiple zeta values of fixed weight, depth, and height
• Relations of multiple zeta values and their algebraic expression.
• On posets and Hopf algebras
• Combinatorial aspects of polylogarithms and Euler-Zagier sums
• Quasi-shuffle products
• On the structure of Hopf algebras
• A note on cyclic gradients
• Periods of mirrors and multiple zeta values
• HARMONIC SUMS, MELLIN TRANSFORMS AND INTEGRALS
• Knots and Feynman Diagrams
• Special values of multiple polylogarithms
• Algebraic relations for multiple zeta values
• Derivation and double shuffle relations for multiple zeta values
• Harmonic Double Series
• Multiple zeta values: an introduction