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A note on evaluations of multiple zeta values
Author(s):
Shuichi
Muneta
Journal:
Proc. Amer. Math. Soc.
137
(2009),
931-935.
MSC (2000):
Primary 11M41;
Secondary 11M06
Posted:
September 25, 2008
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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:
-
- [1]
- 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, No. 2 (1997). MR 1444152 (98b:11091)
- [2]
- J. M. Borwein, D. M. Bradley, D. J. Broadhurst and P. Lisonĕk, Combinatorial aspects of multiple zeta values, Electron. J. Combin. 5, Research Paper 38 (1998). MR 1637378 (99g:11100)
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- J. M. Borwein, D. M. Bradley, D. J. Broadhurst and P. Lisonĕk, Special values of multiple polylogarithms, Trans. Amer. Math. Soc. 353, No. 3 (2001), 907-941. MR 1709772 (2003i:33003)
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- D. Bowman and D. M. Bradley, The algebra and combinatorics of shuffles and multiple zeta values, J. Combin. Theory Ser. A 97 (2002), 43-61. MR 1879045 (2003j:05010)
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- M. Hoffman, Multiple harmonic series, Pacific J. Math. 152 (1992), 275-290. MR 1141796 (92i:11089)
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- K. Ihara, M. Kaneko, and D. Zagier, Derivation and double shuffle relations for multiple zeta values, Compos. Math. 142 (2006), 307-338. MR 2218898 (2007e:11110)
- [8]
- D. Zagier, Values of zeta functions and their applications, First European Congress of Mathematics, Vol. II, Progr. Math., 120, Birkhäuser, Basel, 1994, pp. 497-512. MR 1341859 (96k:11110)
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Additional Information:
Shuichi
Muneta
Affiliation:
Graduate School of Mathematics, Kyushu University, Fukuoka 812-8581, Japan
Email:
muneta@math.kyushu-u.ac.jp
DOI:
10.1090/S0002-9939-08-09592-0
PII:
S 0002-9939(08)09592-0
Keywords:
Multiple zeta values,
shuffle
Received by editor(s):
March 13, 2008,
Received by editor(s) in revised form:
March 29, 2008
Posted:
September 25, 2008
Communicated by:
Ken Ono
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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