×

New families of weighted sum formulas for multiple zeta values. (English) Zbl 1332.05010

Summary: In this paper we shall use the generating functions and the double shuffle relations satisfied by the multiple zeta values to derive some new families of identities of these values.

MSC:

05A15 Exact enumeration problems, generating functions
11M32 Multiple Dirichlet series and zeta functions and multizeta values
PDF BibTeX XML Cite
Full Text: DOI arXiv Euclid

References:

[1] M. Eie, W. Liaw and Y. Ong, A restricted sum formula among multiple zeta values , J. Num. Theor. 129 (2009), 908-921. · Zbl 1183.11053
[2] L. Euler, Meditationes circa singulare serierum genus , Novi Comm. Acad. Sci. Petropol. 20 (1775), 140-186; reprinted in Opera Omnia 15 , B. Teubner, Berlin, 1927.
[3] H. Gangl, M. Kaneko and D. Zagier, Double zeta values and modular forms , in Automorphic forms and zeta functions , S. Böcherer et al., eds., World Scientific, Hackensack, NJ, 2006. · Zbl 1122.11057
[4] A. Granville, A decomposition of Riemann’s zeta-function , in Analytic number theory , Y. Motohashi, ed., Lond. Math. Soc. Lect. Note 247 , Cambridge, 1997. · Zbl 0907.11024
[5] L. Guo and B. Xie, Weighted sum formula for multiple zeta values , J. Num. Theor. 129 (2009), 2747-2765. · Zbl 1229.11117
[6] M.E. Hoffman, Multiple harmonic series , Pac. J. Math. 152 (1992), 275-290. · Zbl 0763.11037
[7] K. Ihara, M. Kaneko and D. Zagier, Derivation and double shuffle relations for multiple zeta values , Compos. Math. 142 (2006), 307-338. · Zbl 1186.11053
[8] T. Machide, Weighted sums with two parameters of multiple zeta values and their formulas , Int. J. Num. Theor. 8 (2012), 1903-1921. · Zbl 1287.11106
[9] —-, Extended double shuffle relations and the generating function of triple zeta values of any fixed weight , Kyushu Math. J. 67 (2013), 281-307. · Zbl 1318.11111
[10] Y. Ohno and W. Zudilin, Zeta stars , Comm. Num. Theor. Phys. 2 (2008), 325-347. · Zbl 1228.11132
[11] D. Zagier, Values of zeta functions and their applications , in First european congress of mathematics , A. Joseph et al., eds., Birkhäuser, Basel, 1994. · Zbl 0822.11001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.