Higher order shuffle regularization for multiple zeta values
HTML articles powered by AMS MathViewer
- by Zhong-hua Li
- Proc. Amer. Math. Soc. 138 (2010), 2321-2333
- DOI: https://doi.org/10.1090/S0002-9939-10-10354-2
- Published electronically: March 10, 2010
- PDF | Request permission
Abstract:
We study the higher order shuffle regularization for multiple zeta values and define higher order regularized shuffle relations. We find that higher order regularized shuffle relations can be deduced from the group-like property of the Drinfel’d associator.References
- P. Deligne and T. Terasoma, Harmonic shuffle relation for associators, preprint, 2005.
- V. G. Drinfel′d, On quasitriangular quasi-Hopf algebras and on a group that is closely connected with $\textrm {Gal}(\overline \textbf {Q}/\textbf {Q})$, Algebra i Analiz 2 (1990), no. 4, 149–181 (Russian); English transl., Leningrad Math. J. 2 (1991), no. 4, 829–860. MR 1080203
- Kentaro Ihara, Masanobu Kaneko, and Don Zagier, Derivation and double shuffle relations for multiple zeta values, Compos. Math. 142 (2006), no. 2, 307–338. MR 2218898, DOI 10.1112/S0010437X0500182X
- Christian Kassel, Quantum groups, Graduate Texts in Mathematics, vol. 155, Springer-Verlag, New York, 1995. MR 1321145, DOI 10.1007/978-1-4612-0783-2
- Jun-Ichi Okuda, Duality formulas of the special values of multiple polylogarithms, Bull. London Math. Soc. 37 (2005), no. 2, 230–242. MR 2119023, DOI 10.1112/S0024609304003996
- Georges Racinet, Doubles mélanges des polylogarithmes multiples aux racines de l’unité, Publ. Math. Inst. Hautes Études Sci. 95 (2002), 185–231 (French, with English and French summaries). MR 1953193, DOI 10.1007/s102400200004
- Christophe Reutenauer, Free Lie algebras, London Mathematical Society Monographs. New Series, vol. 7, The Clarendon Press, Oxford University Press, New York, 1993. Oxford Science Publications. MR 1231799
Bibliographic Information
- Zhong-hua Li
- Affiliation: Graduate School of Mathematical Science, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914, Japan
- Address at time of publication: Department of Mathematics, Tongji University, Shanghai 200092, People’s Republic of China
- Email: lizhmath@gmail.com
- Received by editor(s): September 2, 2009
- Received by editor(s) in revised form: November 5, 2009
- Published electronically: March 10, 2010
- Communicated by: Ken Ono
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 2321-2333
- MSC (2010): Primary 11M32, 33B30
- DOI: https://doi.org/10.1090/S0002-9939-10-10354-2
- MathSciNet review: 2607861