A note on evaluations of multiple zeta values

Muneta, Shuichi

doi:10.1090/S0002-9939-08-09592-0

A note on evaluations of multiple zeta values
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Proc. Amer. Math. Soc. 137 (2009), 931-935 Request permission

Abstract:

In this paper we give a short and simple proof of the remarkable evaluations of multiple zeta values established by D. Bowman and D. M. Bradley.

References

J. M. Borwein, D. M. Bradley, and D. J. Broadhurst, Evaluations of $k$-fold Euler/Zagier sums: a compendium of results for arbitrary $k$, Electron. J. Combin. 4 (1997), no. 2, Research Paper 5, approx. 21. The Wilf Festschrift (Philadelphia, PA, 1996). MR 1444152
Jonathan M. Borwein, David M. Bradley, David J. Broadhurst, and Petr Lisoněk, Combinatorial aspects of multiple zeta values, Electron. J. Combin. 5 (1998), Research Paper 38, 12. MR 1637378
Jonathan M. Borwein, David M. Bradley, David J. Broadhurst, and Petr Lisoněk, Special values of multiple polylogarithms, Trans. Amer. Math. Soc. 353 (2001), no. 3, 907–941. MR 1709772, DOI 10.1090/S0002-9947-00-02616-7
Douglas Bowman and David M. Bradley, The algebra and combinatorics of shuffles and multiple zeta values, J. Combin. Theory Ser. A 97 (2002), no. 1, 43–61. MR 1879045, DOI 10.1006/jcta.2001.3194
Michael E. Hoffman, Multiple harmonic series, Pacific J. Math. 152 (1992), no. 2, 275–290. MR 1141796
Michael E. Hoffman, The algebra of multiple harmonic series, J. Algebra 194 (1997), no. 2, 477–495. MR 1467164, DOI 10.1006/jabr.1997.7127
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
Don Zagier, Values of zeta functions and their applications, First European Congress of Mathematics, Vol. II (Paris, 1992) Progr. Math., vol. 120, Birkhäuser, Basel, 1994, pp. 497–512. MR 1341859