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Higher order shuffle regularization for multiple zeta values

Author: Zhong-hua Li
Journal: Proc. Amer. Math. Soc. 138 (2010), 2321-2333
MSC (2010): Primary 11M32, 33B30
Published electronically: March 10, 2010
MathSciNet review: 2607861
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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 [Enhancements On Off] (What's this?)

  • 1. P. Deligne and T. Terasoma, Harmonic shuffle relation for associators, preprint, 2005.
  • 2. V. Drinfel'd, On quasitriangular quasi-Hopf algebras and on a group that is closely connected with $ \operatorname{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$ (Russian), Algebra i Analiz 2(1990), no. 4, 149-181; translation in Leningrad Math. J. 2(1991), no. 4, 829-860. MR 1080203 (92f:16047)
  • 3. K. Ihara, M. Kaneko and D. Zagier, Derivation and double shuffle relations for multiple zeta values, Compositio Math. 142 (2006), 307-338. MR 2218898 (2007e:11110)
  • 4. C. Kassel, Quantum groups, Graduate Texts in Mathematics, Vol. 155, Springer-Verlag, New York, 1995. MR 1321145 (96e:17041)
  • 5. J. Okuda, Duality formulas of the special values of multiple polylogarithms, Bull. London Math. Soc. 37 (2005), 230-242. MR 2119023 (2006a:11084)
  • 6. G. Racinet, Doubles mélanges des polylogarithmes multiples aux racines de l'unité, Publ. Math. Inst. Hautes Études Sci. 95 (2002), 185-231. MR 1953193 (2004c:11117)
  • 7. C. Reutenauer, Free Lie algebras, Vol. 7 of London Mathematical Society Monographs, The Clarendon Press, Oxford University Press, New York, 1993. MR 1231799 (94j:17002)

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Additional 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

Keywords: Multiple zeta value, shuffle regularization, multiple polylogarithm.
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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