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Evaluations of a class of double  -values
Author(s):
David
Terhune
Journal:
Proc. Amer. Math. Soc.
134
(2006),
1881-1889.
MSC (2000):
Primary 11M41;
Secondary 11B68, 11B75, 11Y35, 33E20
Posted:
December 19, 2005
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Additional information
Abstract:
An analytic proof of an evaluation theorem for the ``convolution"-type double  -values of non-principal characters is given. Along the way, Dirichlet character analogues of generalized single and double polylogarithms are defined. The monodromies of these functions play a pivotal role.
References:
-
- 1.
- T. Arakawa, M. Kaneko, On Multiple
 -values J. Math. Soc. Japan. 56 (2004), no. 4, 967-991. MR 2091412 - 2.
- J. Borwein, D. Broadhurst, J. Kamnitzer, Central Binomial Sums, Multiple Clausen Values, and Zeta Values, Experimental Math., 10 (2001) 1, 25-34. MR 1821569 (2002k:11105)
- 3.
- J. Borwein, R. Girgensohn, Evaluation of Triple Euler Sums, Electron. J. Combin. 3 (1996) 1, Research Paper 23, 27 pp. MR 1401442 (97d:11137)
- 4.
- A. B. Goncharov, Multiple Polylogarithms, Cyclotomy, and Modular Complexes, Math. Res. Lett., 5 (1998) 4, 497-516. MR 1653320 (2000c:11108)
- 5.
- R. Hain, Classical Polylogarithms, Proc. Symp. Pure Math. 55 (1994), 3-42. MR 1265550 (94k:19002)
- 6.
- J. Okuda, Duality Formulas of the Special Values of Multiple Polylogarithms Bull. London Math. Soc. 37 (2005), no. 2, 230-242. MR 2119023
- 7.
- G. Racinet, Doubles Mélanges des Polylogarithmes Multiples aux Racines de L'unité (French) [Double Shuffles of Multiple Polylogarithms at Roots of Unity], Publ. Math. Inst. Hautes Études,, 95 (2002), 185-231. MR 1953193 (2004c:11117)
- 8.
- D. Terhune, Evaluations of Double
 -values, J. Num. Th. 105 (2004), 275-301. MR 2040159 (2005f:11200) - 9.
- H. Tsumura, Combinatorial Relations for Euler-Zagier Sums, Acta Arith. 111 (2004), 27-42. MR 2038060 (2005a:11140)
- 10.
- H. Tsumura, On Mordell-Tornheim Zeta Values, Proc. Amer. Math. Soc. 133 (2005), no. 8, 2387-2393. MR 2138881
- 11.
- D. Zagier, Values of Zeta Functions and their Applications, in: A. Joseph, et al. (Eds.), Proceedings of the First European Congress of Mathematics, Paris, Vol. II (1994), Birkhäuser Verlag, 497-512. MR 1341859 (96k:11110)
- 12.
- J. Zhao, Analytic Continuation of Multiple Polylogarithms, preprint arXiv:math.AG/ 0302054.
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Additional Information:
David
Terhune
Affiliation:
Department of Mathematics, The Pennsylvania State University, 109 McAllister Building, University Park, Pennsylvania 16802
DOI:
10.1090/S0002-9939-05-08261-4
PII:
S 0002-9939(05)08261-4
Keywords:
Multiple $L$-values,
multiple zeta values,
generalized multiple polylogarithm
Received by editor(s):
August 27, 2004
Received by editor(s) in revised form:
February 9, 2005
Posted:
December 19, 2005
Communicated by:
Wen-Ching Winnie Li
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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