Geodesic
Relations for Multiple Zeta Values
Matematičeskie zametki, Tome 84 (2008) no. 6, pp. 825-837.

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We prove new relations for multiple zeta values. In particular, they imply Vasilev's equality and a formula for the summation of multiple zeta values of fixed weight with a constraint on the first coordinate.
Keywords: zeta function, multiple zeta values, Fubini's theorem, stuffle product (harmonic product) of zeta values, generating function. 
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     title = {Relations for {Multiple} {Zeta} {Values}},
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S. A. Zlobin. Relations for Multiple Zeta Values. Matematičeskie zametki, Tome 84 (2008) no. 6, pp. 825-837. http://geodesic.mathdoc.fr/item/MZM_2008_84_6_a2/

[1] S. A. Zlobin, “Proizvodyaschie funktsii dlya znachenii kratnoi dzeta-funktsii”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2005, no. 2, 55–59 | MR | Zbl

[2] D. V. Vasilev, “Nekotorye formuly dlya dzeta-funktsii Rimana v tselykh tochkakh”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1996, no. 1, 81–84 | MR | Zbl

[3] S. A. Zlobin, “O nekotorykh integralnykh tozhdestvakh”, UMN, 57:3 (2002), 153–154 | MR | Zbl

[4] M. E. Hoffman, “The algebra of multiple harmonic series”, J. Algebra, 194:2 (1997), 477–495 | DOI | MR | Zbl

[5] E. A. Ulanskii, “Tozhdestva dlya obobschennykh polilogarifmov”, Matem. zametki, 73:4 (2003), 613–624 | MR | Zbl

[6] A. Granville, “A decomposition of Riemann's zeta-function”, Analytic Number Theory (Kyoto, 1996), London Math. Soc. Lecture Note Ser., 247, Cambridge Univ. Press, Cambridge, 1997, 95–101 | MR | Zbl

[7] Y. Ohno, “A generalization of the duality and sum formulas on the multiple zeta values”, J. Number Theory, 74:1 (1999), 39–43 | DOI | MR | Zbl

[8] T. Arakawa, M. Kaneko, “Multiple zeta-values, poly-Bernoulli numbers, and related zeta functions”, Nagoya Math. J., 153 (1999), 1–21 | MR | Zbl

[9] T. Aoki, Y. Ohno, “Sum relations for multiple zeta values and connection formulas for the Gauss hypergeometric functions”, Publ. Res. Inst. Math. Sci., 41:2 (2005), 329–337 ; arXiv: math/0307264v1 | DOI | MR | Zbl