caa a22 4500 445835532 CHVBK 20180317145329.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s00209-010-0705-6 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0705-6 Shuffle products for multiple zeta values and partial fraction decompositions of zeta-functions of root systems [Elektronische Daten] [Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura] The shuffle product plays an important role in the study of multiple zeta values (MZVs). 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 MZVs of root systems. As an application, we give a proof of extended double shuffle relations without using Drinfel'd integral expressions for MZVs. Furthermore, our argument enables us to give some functional relations which include double shuffle relations. Springer-Verlag, 2010 Multiple zeta values nationallicence Witten zeta-functions nationallicence Root systems nationallicence Komori Yasushi Department of Mathematics, Rikkyo University, Nishi-Ikebukuro, Toshima-ku, 171-8501, Tokyo, Japan aut Matsumoto Kohji Graduate School of Mathematics, Nagoya University, Chikusa-ku, 464-8602, Nagoya, Japan aut Tsumura Hirofumi Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1, Minami-Ohsawa, 192-0397, Hachioji, Tokyo, Japan aut Mathematische Zeitschrift Springer-Verlag 268/3-4(2011-08-01), 993-1011 0025-5874 268:3-4<993 2011 268 209 https://doi.org/10.1007/s00209-010-0705-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0705-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Komori Yasushi Department of Mathematics, Rikkyo University, Nishi-Ikebukuro, Toshima-ku, 171-8501, Tokyo, Japan aut NATIONALLICENCE 700 1- Matsumoto Kohji Graduate School of Mathematics, Nagoya University, Chikusa-ku, 464-8602, Nagoya, Japan aut NATIONALLICENCE 700 1- Tsumura Hirofumi Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1, Minami-Ohsawa, 192-0397, Hachioji, Tokyo, Japan aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 268/3-4(2011-08-01), 993-1011 0025-5874 268:3-4<993 2011 268 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer