[Sur l'algèbre des multizêtas de Hurwitz]
Les multizêtas sont des nombres réels possédant une structure d'algèbre complexe : il existe deux produits interagissant. Il est naturel de définir un analogue fonctionnel de ces nombres pour en avoir une meilleure compréhension, ce qui conduit aux multizêtas de Hurwitz, dont on souhaiterait connaître précisémment la structure d'algèbre. Dans cette note, nous montrons que l'algèbre des multizêtas de Hurwitz est une algèbre de polynômes.
Multizeta values are real numbers that span a complicated algebra: there exist two different interacting products. A functional analog of these numbers is defined so as to obtain a better understanding of them, the Hurwitz multizeta functions, which span an algebra for which a precise description is wanted. In this note, we prove that the algebra of Hurwitz multizeta functions is a polynomial algebra.
Accepté le :
Publié le :
@article{CRMATH_2014__352_11_865_0,
author = {Bouillot, Olivier},
title = {The algebra of {Hurwitz} multizeta functions},
journal = {Comptes Rendus. Math\'ematique},
pages = {865--869},
publisher = {Elsevier},
volume = {352},
number = {11},
year = {2014},
doi = {10.1016/j.crma.2014.09.006},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2014.09.006/}
}
TY - JOUR AU - Bouillot, Olivier TI - The algebra of Hurwitz multizeta functions JO - Comptes Rendus. Mathématique PY - 2014 SP - 865 EP - 869 VL - 352 IS - 11 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2014.09.006/ DO - 10.1016/j.crma.2014.09.006 LA - en ID - CRMATH_2014__352_11_865_0 ER -
Bouillot, Olivier. The algebra of Hurwitz multizeta functions. Comptes Rendus. Mathématique, Tome 352 (2014) no. 11, pp. 865-869. doi : 10.1016/j.crma.2014.09.006. http://www.numdam.org/articles/10.1016/j.crma.2014.09.006/
[1] Algebraic Combinatorics and Coinvariant Spaces, CMS Treatise in Mathematics, CRC Press, Boca Raton, FL, USA, 2009 (221 p)
[2] Invariants analytiques des difféomorphismes et multizêtas, 2011 (PhD thesis Orsay, France, 291 p)
[3] The algebra of multitangent functions, J. Algebra, Volume 410 (2014), pp. 148-238
[4] Mixed Tate motives over , Ann. of Math. (2), Volume 175 (2012) no. 2, pp. 949-976
[5] On the decomposition of motivic multiple zeta values (Nakamura, H. et al., eds.), Galois–Teichmüller Theory and Arithmetic Geometry, Adv. Stud. Pure Math., vol. 68, 2012, pp. 31-58
[6] Fonctions polylogarithmes, nombres polyzeta et groupes pro-unipotents, Séminaire N. Bourbaki, World Scientific, Singapore, 2000, pp. 137-173 (exp. 885)
[7] Quasi-shuffles, mixable shuffles and Hopf algebras, J. Algebr. Comb., Volume 24 (2006), pp. 83-101
[8] Combinatorial study of colored Hurwitz polyzêtas, Discrete Math., Volume 312 (2013) no. 24, pp. 3489-3497
[9] Multipartite P-partitions and inner products of skew Schur functions, Combinatorics and Algebra, Boulder, CO, USA, 1983, pp. 289-317 Contemp. Math., 34 (1984) 289–301
[10] Quasi-shuffle products, J. Algebr. Comb., Volume 11 (2000), pp. 49-68
[11] An algebraic version of the Knizhnik–Zamolodchikov equation, Ramanujan J., Volume 28 (2012) no. 3, pp. 361-384
[12] De l'algèbre des ζ de Riemann multivariées à l'algèbre des ζ de Hurwitz multivariées, Sémin. Lothar. Comb., Volume 44 (2000) Art. B44i, 21 p. (electronic)
[13] Multiple Hurwitz zeta function, Multiple Dirichlet Series, Automorphic Forms and Analytic Number Theory, Proc. Symp. Pure Math., vol. 75, 2006, pp. 135-156
[14] Free Lie Algebras, Lond. Math. Soc. Monogr. New. Ser., vol. 7, Oxford Sciences Publications, Oxford, UK, 1993
[15] Valeurs zêta multiples. Une introduction, J. Théor. Nr. Bordx., Volume 12 (2000), pp. 581-592
[16] Algebraic relations for multiple zeta values, Russ. Math. Surv., Volume 58 (2003), pp. 1-29
Cité par Sources :
