Comptes Rendus
no. 12
Number theory
Multiple zeta values at the non-positive integers
[Les valeurs de la fonction zêta multiple aux entiers négatifs]

Présenté par : the Editorial Board

Boualem Sadaoui1
1 Université de Khemis Miliana, Laboratoire LESI, 44225, Khemis Miliana, Algeria
Comptes Rendus. Mathématique, Volume 352 (2014) no. 12, pp. 977-984.

Dans cet article, nous proposons une autre méthode pour calculer les valeurs de la fonction zêta multiple aux entiers négatifs à l'aide de la formule de Raabe et des nombres de Bernoulli.

In this paper, we provide an alternative method to calculate the multiple zeta values at non-positive integers by means of Raabe's formula and the Bernoulli numbers.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.10.001
Boualem Sadaoui 1

1 Université de Khemis Miliana, Laboratoire LESI, 44225, Khemis Miliana, Algeria 
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Boualem Sadaoui. Multiple zeta values at the non-positive integers. Comptes Rendus. Mathématique, Volume 352 (2014) no. 12, pp. 977-984. doi : 10.1016/j.crma.2014.10.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.10.001/

[1] S. Akiyama; S. Egami; Y. Tanigawa Analytic continuation of multiple zeta-functions and their values at non-positive integers, Acta Arith., Volume 98 (2001) no. 2, pp. 107-116

[2] T.M. Apostol Introduction to Analytic Number Theory, Springer, 1976

[3] F.V. Atkinson The mean-value of the Riemann zeta function, Acta Math., Volume 81 (1949), pp. 353-376

[4] J.M. Borwein; D.M. Bradley; D.J. Broadhurst; P. Lisoněk Combinatorial aspects of multiple zeta values, Electron. J. Comb., Volume 5 (1998), pp. 1077-8926

[5] L. Euler Meditationes circa singulare serierum genus, Novi Commun. Acad. Sci. Petropol., Volume 20 (1775), pp. 140-186 (reprinted in Opera Omnia, Ser. I, vol. 15, B.G. Teubner, Berlin, 1927, pp. 217–267)

[6] E. Friedman; A. Pereira Special values of Dirichlet series and zeta integrals, Int. J. Number Theory, Volume 8 (2012) no. 3, pp. 697-714

[7] E. Friedman; S. Ruijsenaars Shintani–Barnes zeta and gamma functions, Adv. Math., Volume 187 (2004), pp. 362-395

[8] A. Granville A decomposition of Riemann's Zeta-function (Y. Motohashi, ed.), Analytic Number Theory, London Mathematical Society Lecture Note Series, vol. 247, Cambridge University Press, 1997, pp. 95-101

[9] L. Guo; B. Zhang Renormalization of multiple zeta values, J. Algebra, Volume 319 (2008) no. 9, pp. 3770-3809

[10] M. Hoffman Multiple harmonic series, Pac. J. Math., Volume 152 (1992), pp. 257-290

[11] D. Manchon; S. Paycha Nested sums of symbols and renormalised multiple zeta functions, Int. Math. Res. Not., Volume 24 (2010), pp. 4628-4697

[12] K. Matsumoto Analytic continuation of multiple zeta functions, Proc. Amer. Math. Soc., Volume 128 (2003), pp. 223-243

[13] Y. Ohno A generalization of the duality and sum formula on the multiple zeta values, J. Number Theory, Volume 101 (1999), pp. 39-43

[14] D. Zagier Periods of modular forms, traces of Hecke operators and multiple zeta values, Kyoto, 1992, Volume vol. 843 (1993), pp. 162-170

[15] D. Zagier Values of zeta functions and their applications (A. Joseph et al., eds.), First European Congress of Mathematics (Paris, 1992), Vol. II, Birkhäuser, Basel, 1994, pp. 497-512

[16] J.Q. Zhao Analytic continuation of multiple zeta functions, Proc. Amer. Math. Soc., Volume 128 (2000), pp. 1275-1283

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