2009/08/05 by Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebra over a field #Analytic Number Theory Research #Commutative property #Fraction (chemistry) #Free product #Geometry #Group (periodic table) #Interpretation (philosophy) #Mathematics #Product (mathematics) #Pure mathematics #Rational number #Root (linguistics) #Root of unity #math.NT #msc:11M41 #msc:17B20 #msc:40B05
paper · pdf · doi:10.1007/s00209-010-0705-6
published as Math. Zeitschrift 268 (2011), 993-1011 · 18 pages
arxiv created 2009/08/05 · openalex publication_date 2010/03/24 · arxiv updated 2016/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The shuffle product plays an important role in the study of multiple zeta values. This is expressed in terms of multiple integrals, and also as a product in a certain non-commutative polynomial algebra over the rationals in two indeterminates. In this paper, we give a new interpretation of the shuffle product. In fact, we prove that the procedure of shuffle products essentially coincides with that of partial fraction decompositions of multiple zeta values of root systems. As an application, we give a proof of extended double shuffle relations without using Drinfel'd integral expressions for multiple zeta values. Furthermore, our argument enables us to give some functional relations which include double shuffle relations.