Abstract
The present article deals with various generating series and group schemes (not necessarily affine ones) associated with MZVs. Our developments are motivated by Ecalle’s mould calculus approach to the latter. We propose in particular a Hopf algebra–type encoding of symmetril moulds and introduce a new resummation process for MZVs.
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References
Aguiar, M., Mahajan, S.: Monoidal functors, species and Hopf algebras. CRM Monogr. Ser. 29 (2010)
Cartier, P.: A primer of Hopf algebras. Frontiers in Number Theory, Physics, and Geometry II, pp. 537–615. Springer, Berlin (2007)
Cartier, P.: Fonctions polylogarithmes, nombres polyzêtas et groupes prounipotents, Séminaire Bourbaki, Mars 2001, 53ème année, 2000–2001, no 885
Cresson, J.: Calcul moulien. Annales de la Faculté des Sciences de Toulouse. Mathématiques 18(2), 307–395 (2009)
Ebrahimi-Fard, K., Guo, L.: Multiple zeta values and Rota-Baxter algebras. Integers 8(2), 1553–1732 (2008)
Ebrahimi-Fard, K., Patras, F.: La structure combinatoire du calcul intégral. Gazette des Mathématiciens 138 (2013)
Ecalle, J.: ARI/GARI, la dimorphie et l’arithmétique des multizêtas: un premier bilan. Journal de Théorie des Nombres Bordeaux 15(2), 411–478 (2003)
Foissy, L., Patras, F.: Natural endomorphisms of shuffle algebras. Int. J. Algebra Comput. 23(4), 989–1009 (2013)
Foissy, L., Patras, F., Thibon, J.-Y.: Deformations of shuffles and quasi-shuffles. Annales de l’Institut Fourier (Grenoble) 66(1), 209–237 (2016)
Furusho, H.: Double shuffle relation for associators. Ann. Math. 174, 341–360 (2011)
Hoffman, M.E.: Quasi-shuffle products. J. Algebr. Comb. 11(1), 49–68 (2000)
Ihara, K., Kaneko, M., Zagier, D.: Derivation and double shuffle relations for multiple zeta values. Compos. Math. 142, 307–338 (2006)
Patras, F.: Generic algebras and iterated Hochschild homology. J. Pure Appl. Algebra 162, 337–357 (2001)
Patras, F., Reutenauer, C.: On descent algebras and twisted bialgebras. Moscow Math. J. 4(1), 199–216 (2004)
Patras, F., Schocker, M.: Twisted descent algebras and the Solomon-Tits algebra. Adv. Math. 199(1), 151–184 (2006)
Patras, F., Schocker, M.: Trees, set compositions and the twisted descent algebra. J. Algebr. Comb. 28, 3–23 (2008)
Peskin, M.E., Schroeder, D.V.: An Introduction to Quantum Field Theory. Westview (1995)
Racinet, G.: Doubles mélanges des polylogarithmes multiples aux racines de l’unité. Publications Mathématiques de l’Institut des Hautes Études Scientifiques 95(1), 185–231 (2002)
Reutenauer, C.: Free Lie Algebras. Oxford University Press (1993)
Acknowledgements
The authors acknowledge support from ICMAT, Madrid, and from the grant CARMA, ANR-12-BS01-0017.
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Malvenuto, C., Patras, F. (2020). Symmetril Moulds, Generic Group Schemes, Resummation of MZVs. In: Burgos Gil, J., Ebrahimi-Fard, K., Gangl, H. (eds) Periods in Quantum Field Theory and Arithmetic. ICMAT-MZV 2014. Springer Proceedings in Mathematics & Statistics, vol 314. Springer, Cham. https://doi.org/10.1007/978-3-030-37031-2_14
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DOI: https://doi.org/10.1007/978-3-030-37031-2_14
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