Doubles mélanges des polylogarithmes multiples aux racines de l’unité

 Access to full text

 Full (PDF)

1. [1] D. BAR-NATAN, Non-associative tangles, Geometric topology (Athens, GA, 1993), Amer. Math. Soc., Providence, RI, 1997, pp. 139-183. Zbl0888.57008MR1470726
2. [2] D. BAR-NATAN, On associators and the Grothendieck-Teichmüller group. I, Selecta Math. (N.S.) 4, No. 2 (1998), 183-212, arXiv:q-alg/960621. Zbl0974.16028MR1669949
3. [3] M. BIGOTTE, G. JACOB, N. OUSSOUS and M. PETITOT, Tables des relations de la fonction zêta colorée, prépublication du LIFL, Université Lille I, 1998. 
4. [4] L. BOUTET DE MONVEL, Remarques sur les séries logarithmiques divergentes, Exposé au colloque « polylogarithmes et conjecture de Deligne-Ihara » au C.I.R.M. (Luminy), http://www.math.jussieu.fr/~boutet, avril 2000. 
5. [5] D. J. BROADHURST, Conjectured enumeration of irreducible multiple zeta values, from knots and Feynman diagrams, Publication électronique, décembre 1996, arXiv:hep-th/9612012. 
6. [6] P. CARTIER, Construction combinatoire des invariants de Vassiliev-Kontsevich des noeuds, R.C.P. 25, Vol. 45 (French) (Strasbourg, 1992-1993), Univ. Louis Pasteur, Strasbourg, 1993, pp. 1-10. MR1331627
7. [7] K.-T. CHEN, Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula, Ann. of Math. (2) 65 (1957), 163-178. Zbl0077.25301MR85251
8. [8] K. T. CHEN, Iterated path integrals, Bull. Amer. Math. Soc. 83, no. 5 (1977), 831-879. Zbl0389.58001MR454968
9. [9] P. DELIGNE, Le groupe fondamental de la droite projective moins trois points, Galois groups over Q (Berkeley, CA, 1987), Springer, New York, 1989, pp. 79-297. Zbl0742.14022MR1012168
10. [10] P. DELIGNE, Multizeta values, Notes d’exposés, IAS, Princeton, 2001. 
11. [11] P. DELIGNE, Communication personelle, juin 2001. 
12. [12] M. DEMAZURE and P. GABRIEL, Groupes algébriques. Tome I : Géométrie algébrique, généralités, groupes commutatifs, Masson & Cie, Paris, 1970. Zbl0203.23401MR302656
13. [13] V. G. DRINFELD, On quasitriangular quasi-Hopf algebras and a group closely related to Gal$(\overline{Q}/Q)$, Leningrad Mathematical Journal 2 (1991), 829-860. Zbl0728.16021MR1080203
14. [14] J. ÉCALLE, La libre génération des multizêtas et leur décomposition canonico-explicite en irréductibles, Notes de séminaire, automne 1999. 
15. [15] M. ESPIE, J.-C. NOVELLI and G. RACINET, Experimental results about double shuffles of polyzetas, En préparation. 
16. [16] P. ETINGOF and D. KAZHDAN, Quantization of Lie bialgebras. I, Selecta Math. (N.S.) 2, No. 1 (1996), 1-41, arXiv:q-alg/9506005. Zbl0863.17008MR1403351
17. [17] I. GELFAND, D. KROB, A. LASCOUX, B. LECLERC, V. RETAKH and J. THIBON, Non-commutative symmetric func- tions, Advances in Mathematics 112 (1995), 218-348. Zbl0831.05063MR1327096
18. [18] M. GERSTENHABER, The cohomology structure of an associative ring, Ann. of Math. (2) 78 (1963), 267-288. Zbl0131.27302MR161898
19. [19] A. B. GONCHAROV, Multiple polylogarithms, cyclotomy and modular complexes, Mathematical Research Letters 5 (1998), 497-516. Zbl0961.11040MR1653320
20. [20] A. B. GONCHAROV, The dihedral Lie algebras and Galois symmetries of ${\pi }_1^{\left(l\right)}({\mathbb{P}}^1-(\{0,\infty \}\cup {\mu }_N))$, Duke Math. J. 110, no. 3 (2001), 397-487, arXiv:math.AG/0009121. Zbl1113.14020
21. [21] A. B. GONCHAROV, Multiple polylogarithms and mixed Tate motives, Publication électronique, mars 2001, arXiv:math.AG/0103059. 
22. [22] R. HAIN and M. MATSUMOTO, Weighted completion of Galois groups and some conjectures of Deligne, Publication électronique, juin 2000, arXiv:math.AG/0006158. 
23. [23] M. HOANG NGOC and M. PETITOT, Lyndon words, polylogarithms and the Riemann zeta function, Discrete Mathematics 217 (1-3) (2000), 273-292. Zbl0959.68144MR1766271
24. [24] M. HOFFMAN, The algebra of multiple harmonic series, Journal of Algebra 194, no. 2 (1997), 477-495. Zbl0881.11067MR1467164
25. [25] K. IHARA and M. KANEKO, Derivation relations and regularized double shuffle relations of multiple zeta values, Prépublication, Univ. Kyushu, 2000. Zbl1186.11053
26. [26] Y. IHARA, Automorphisms of pure sphere braid groups and Galois representations, The Grothendieck Festschrift, Vol. II, Birkhäuser Boston, Boston, MA, 1990, pp. 353-373. Zbl0728.20033MR1106903
27. [27] Y. IHARA, Braids, Galois groups, and some arithmetic functions, 1990 Int. Cong. of Mathematicians, Math. Soc. of Japan, Tokyo, 1991, pp. 99-120. Zbl0757.20007MR1159208
28. [28] Y. IHARA, On the stable derivation algebra associated with some braid groups, Israel J. Math. 80, no. 1-2 (1992), pp. 135-153, Zbl0782.20034MR1248930
29. [29] Y. IHARA and M. MATSUMOTO, On Galois actions on profinite completions of braid groups, Recent developments in the inverse Galois problem (Seattle, WA, 1993), Amer. Math. Soc., Providence, RI, 1995, pp. 173-200. Zbl0848.11058MR1352271
30. [30] M. KONTSEVITCH, Operads and motives in deformation quantization, Lett. Math. Phys. 48, no. 1 (1999), 35-72, Moshé Flato (1937-1998). Zbl0945.18008MR1718044
31. [31] T. T. Q . LE and J. MURAKAMI, Kontsevich’s integral for the Kauffman polynomial, Nagoya Math. J. 142 (1996), 39-65. Zbl0866.57008
32. [32] C. MALVENUTO and C. REUTENAUER, Duality between quasi-symmetric functions and the Solomon descent algebra, Journal of Algebra 177, no. 3 (1995), 967-982. Zbl0838.05100MR1358493
33. [33] G. RACINET, Séries génératrices non-commutatives de polyzêtas et associateurs de Drinfel’d, Thèse de doctorat, Université de Picardie-Jules-Verne, 2000, http://www.dma.ens.fr/~racinet. 
34. [34] G. RACINET, Torseurs associés à certaines relations algébriques entre polyzêtas aux racines de l’unité, Comptes-rendus de l’Académie des Sciences, Série I 333, no. 1 (2001), 5-10, arXiv:math.QA/0012024. Zbl1033.11033
35. [35] G. RACINET, Algèbres de Lie des valeurs formelles d’hyperlogarithmes aux racines de l’unité, Comptes-rendus de l’Académie des Sciences, Série I 333, no. 1 (2001), 11-16, arXiv:math.QA/0012024. Zbl1033.11032
36. [36] R. REE, Lie elements and an algebra associated with shuffles, Ann. of Math. (2) 68 (1958), 210-220. Zbl0083.25401MR100011
37. [37] C. REUTENAUER, Free Lie algebras, London Mathematical Society Monographs, New series, no. 7, Oxford, 1993. Zbl0798.17001MR2035110
38. [38] D. E. TAMARKIN, Formality of Chain Operad of Small Squares, Publication électronique, septembre 1998, arXiv:math.QA/9809164. 
39. [39] D. ZAGIER, Values of zeta functions and their applications, First European Congress of Mathematics, Vol. II (Paris, 1992), Birkhäuser, Basel, 1994, pp. 497-512. Zbl0822.11001MR1341859

1. Jean-Christophe Novelli, Frédéric Patras, Jean-Yves Thibon, Natural endomorphisms of quasi-shuffle Hopf algebras
2. Pierre Deligne, Alexander B. Goncharov, Groupes fondamentaux motiviques de Tate mixte
3. J. Cresson, S. Fischler, T. Rivoal, Séries hypergéométriques multiples et polyzêtas
4. Francis C. S. Brown, Multiple zeta values and periods of moduli spaces ${\overline{𝔐}}_{0,n}$