Livres, Actes et Séminaires du Centre Mersenne

[And04] Y. André Une introduction aux motifs (motifs purs, motifs mixtes, périodes), Panoramas & Synthèses, 17, Société Mathématique de France, Paris, 2004

[And09] Y. André Galois theory, motives and transcendental numbers, Renormalization and Galois theories (IRMA Lect. Math. Theor. Phys.), Volume 15, European Mathematical Society, Zürich, 2009, pp. 165-177 | DOI | Zbl

[And17] Y. André Groupes de Galois motiviques et périodes, Séminaire Bourbaki. Vol. 2015/16 (Astérisque), Volume 390, Société Mathématique de France, Paris, 2017, pp. 1-26 (Exp. No. 1104) | Zbl

[Apé79] R. Apéry Irrationalité de $\zeta 2$ et $\zeta 3$, Journées arithmétiques de Luminy (Astérisque), Volume 61, Société Mathématique de France, Paris, 1979, pp. 11-13 | Zbl

[BB03] P. Belkale; P. Brosnan Matroids motives, and a conjecture of Kontsevich, Duke Math. J., Volume 116 (2003) no. 1, pp. 147-188 | DOI | Zbl

[BBV10] J. Blümlein; D. J. Broadhurst; J. A. M. Vermaseren The multiple zeta value data mine, Comput. Phys. Comm., Volume 181 (2010) no. 3, pp. 582-625 | DOI | Zbl

[BEK06] S. Bloch; H. Esnault; D. Kreimer On motives associated to graph polynomials, Comm. Math. Phys., Volume 267 (2006) no. 1, pp. 181-225 | DOI | Zbl

[Beu79] F. Beukers A note on the irrationality of $\zeta \left(2\right)$ and $\zeta \left(3\right)$, Bull. London Math. Soc., Volume 11 (1979) no. 3, pp. 268-272 | DOI | Zbl

[BF89] D. H. Bailey; H. R. P. Ferguson Numerical results on relations between fundamental constants using a new algorithm, Math. Comput., Volume 53 (1989) no. 188, pp. 649-656 | DOI | Zbl

[BF91] D. H. Bailey; H. R. P. Ferguson A polynomial time, numerically stable integer relation algorithm (1991) (Report SRC-TR-92-066, Supercomputing Research Center, 14 p.)

[BGF] J. I. Burgos Gil; J. Fresán Multiple zeta values : from numbers to motives (livre à paraître dans la série Clay Mathematics Proceedings)

[BK97] D. J. Broadhurst; D. Kreimer Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops, Phys. Lett. B, Volume 393 (1997) no. 3-4, pp. 403-412 | DOI | Zbl

[Bor77] A. Borel Cohomologie de ${\mathrm{SL}}_n$ et valeurs de fonctions zeta aux points entiers, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), Volume 4 (1977) no. 4, pp. 613-636 | Zbl

[BR01] K. Ball; T. Rivoal Irrationalité d’une infinité de valeurs de la fonction zêta aux entiers impairs, Invent. Math., Volume 146 (2001) no. 1, pp. 193-207 | DOI | Zbl

[Bro12a] F. Brown Mixed Tate motives over $\mathbb{Z}$, Ann. of Math. (2), Volume 175 (2012) no. 2, pp. 949-976 | DOI | Zbl

[Bro12b] F. Brown On the decomposition of motivic multiple zeta values, Galois-Teichmüller theory and arithmetic geometry (Adv. Stud. Pure Math.), Volume 63, Math. Soc. Japan, Tokyo, 2012, pp. 31-58 | DOI | Zbl

[Bro17] F. Brown Feynman amplitudes, coaction principle, and cosmic Galois group, Commun. Number Theory Phys., Volume 11 (2017) no. 3, pp. 453-556 | DOI | Zbl

[BS03] La fonction zêta (N. Berline; C. Sabbah, eds.), Journées X-UPS, Les Éditions École polytechnique, Palaiseau, 2003

[BS12] F. Brown; O. Schnetz A K3 in ${\varphi }^4$, Duke Math. J., Volume 161 (2012) no. 10, pp. 1817-1862 | DOI | Zbl

[Car01] P. Cartier A mad day’s work : from Grothendieck to Connes and Kontsevich. The evolution of concepts of space and symmetry, Bull. Amer. Math. Soc. (N.S.), Volume 38 (2001) no. 4, pp. 389-408 | DOI | Zbl

[Che77] K.-T. Chen Iterated path integrals, Bull. Amer. Math. Soc. (N.S.), Volume 83 (1977) no. 5, pp. 831-879 | DOI | Zbl

[Del74] P. Deligne La conjecture de Weil. I, Publ. Math. Inst. Hautes Études Sci. (1974) no. 43, pp. 273-307 | DOI | Numdam | Zbl

[Del80] P. Deligne La conjecture de Weil. II, Publ. Math. Inst. Hautes Études Sci. (1980) no. 52, pp. 137-252 | DOI | Numdam | Zbl

[Del89] P. Deligne Le groupe fondamental de la droite projective moins trois points, Galois groups over $\mathbf{Q}$ (Berkeley, CA, 1987) (Math. Sci. Res. Inst. Publ.), Volume 16, Springer, New York, 1989, pp. 79-297 | DOI | Zbl

[DG05] P. Deligne; A. B. Goncharov Groupes fondamentaux motiviques de Tate mixte, Ann. Sci. École Norm. Sup. (4), Volume 38 (2005) no. 1, pp. 1-56 | DOI | Numdam | Zbl

[DR31] G. De Rham Sur l’analysis situs des variétés à $n$ dimensions, Doctorat d’État, Faculté des Sciences de Paris (1931) (http://www.numdam.org/item/THESE_1931__129__1_0)

[Dri91] V. G. Drinfel’d On quasitriangular quasi-Hopf algebras and a group closely connected with $\text{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$, Leningrad Math. J., Volume 2 (1991) no. 4, pp. 829-860 | Zbl

[Eul38] L. Euler De summatione innumerabilium progressionum, Commentarii academiae scientiarum Petropolitanae (1738), pp. 91-105

[Eul40] L. Euler De summis serierum reciprocarum, Commentarii academiae scientiarum Petropolitanae (1740), pp. 123-134

[Fis04] S. Fischler Irrationalité de valeurs de zêta (d’après Apéry, Rivoal,...), Séminaire Bourbaki (Astérisque), Volume 294, Société Mathématique de France, Paris, 2004, pp. 27-62 | Zbl

[GKZ06] H. Gangl; M. Kaneko; D. Zagier Double zeta values and modular forms, Automorphic forms and zeta functions, World Sci. Publ., Hackensack, NJ, 2006, pp. 71-106 | DOI | Zbl

[Gon01a] 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., Volume 110 (2001) no. 3, pp. 397-487 | DOI | Zbl

[Gon01b] A. B. Goncharov Multiple polylogarithms and mixed Tate motives, 2001 | arXiv

[Gon01c] A. B. Goncharov Multiple $\zeta$-values, Galois groups, and geometry of modular varieties, European Congress of Mathematics (Barcelona, July 10–14, 2000), Vol. I, Birkhäuser Basel, Basel, 2001, pp. 361-392 | Zbl

[Gon05] A. B. Goncharov Galois symmetries of fundamental groupoids and noncommutative geometry, Duke Math. J., Volume 128 (2005) no. 2, pp. 209-284 | DOI | Zbl

[Gro66] A. Grothendieck On the de Rham cohomology of algebraic varieties, Publ. Math. Inst. Hautes Études Sci. (1966) no. 29, pp. 95-103 | DOI | Numdam | Zbl

[Gro68] A. Grothendieck Formule de Lefschetz et rationalité des fonctions $L$, Dix exposés sur la cohomologie des schémas (Adv. Stud. Pure Math.), Volume 3, North-Holland, Amsterdam, 1968, pp. 31-45 | Zbl

[Hai86] R. M. Hain Mixed Hodge structures on homotopy groups, Bull. Amer. Math. Soc. (N.S.), Volume 14 (1986) no. 1, pp. 111-114 | DOI | Zbl

[Hai87a] R. M. Hain The de Rham homotopy theory of complex algebraic varieties. I, $K$-Theory, Volume 1 (1987) no. 3, pp. 271-324 | DOI | Zbl

[Hai87b] R. M. Hain The geometry of the mixed Hodge structure on the fundamental group, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985) (Proc. Sympos. Pure Math.), Volume 46, American Mathematical Society, Providence, RI, 1987, pp. 247-282 | Zbl

[HJPO99] Hoang Ngoc Minh; G. Jacob; M. Petitot; N. E. Oussous Aspects combinatoires des polylogarithmes et des sommes d’Euler-Zagier, Sém. Lothar. Combin., Volume 43 (1999), B43e, 29 pages | Zbl

[HMS17] A. Huber; S. Müller-Stach Periods and Nori motives, Ergeb. Math. Grenzgeb. (3), 65, Springer, Cham, 2017 | DOI

[Hof97] M. E. Hoffman The algebra of multiple harmonic series, J. Algebra, Volume 194 (1997) no. 2, pp. 477-495 | DOI | Zbl

[Hof00] M. E. Hoffman Quasi-shuffle products, J. Algebraic Combin., Volume 11 (2000) no. 1, pp. 49-68 | DOI | Zbl

[HZ87] R. M. Hain; S. Zucker Unipotent variations of mixed Hodge structure, Invent. Math., Volume 88 (1987) no. 1, pp. 83-124 | DOI | Zbl

[IKZ06] K. Ihara; M. Kaneko; D. Zagier Derivation and double shuffle relations for multiple zeta values, Compositio Math., Volume 142 (2006) no. 2, pp. 307-338 | DOI | Zbl

[KZ01] M. Kontsevich; D. Zagier Periods, Mathematics unlimited—2001 and beyond, Springer, Berlin, 2001, pp. 771-808 | DOI | Zbl

[Lin82] F. Lindemann Ueber die Zahl $\pi$, Math. Ann., Volume 20 (1882) no. 2, pp. 213-225 | DOI

[PS16] E. Panzer; O. Schnetz The Galois coaction on ${\varphi }^4$ periods, Commun. Number Theory Phys., Volume 11 (2016), pp. 657-705 | DOI | Zbl

[Reu93] C. Reutenauer Free Lie algebras, London Math. Soc. Monographs, 7, The Clarendon Press, Oxford University Press, New York, 1993 | DOI

[Riv00] T. Rivoal La fonction zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs, C. R. Acad. Sci. Paris Sér. I Math., Volume 331 (2000) no. 4, pp. 267-270 | DOI | Zbl

[Riv19] T. Rivoal Les $E$-fonctions et $G$-fonctions de Siegel, Périodes et transcendence (Journées X-UPS), Les Éditions de l’École polytechnique, Palaiseau, 2019 (ce volume) | DOI

[Rud87] W. Rudin Real and complex analysis, McGraw-Hill Book Co., New York, 1987

[Sou10] I. Soudères Motivic double shuffle, Int. J. Number Theory, Volume 6 (2010) no. 2, pp. 339-370 | DOI | Zbl

[Sti30] J. Stirling Methodus differentialis, sive Tractatus de summatione et interpolatione serierum infinitarum, G. Bowyer, impensis G. Strahan (Londini), 1730

[Ter02] T. Terasoma Mixed Tate motives and multiple zeta values, Invent. Math., Volume 149 (2002) no. 2, pp. 339-369 | DOI | Zbl

[Voe00] V. Voevodsky Triangulated categories of motives over a field, Cycles, transfers, and motivic homology theories (Ann. of Math. Stud.), Volume 143, Princeton Univ. Press, Princeton, NJ, 2000, pp. 188-238 | Zbl

[Wei49] A. Weil Numbers of solutions of equations in finite fields, Bull. Amer. Math. Soc., Volume 55 (1949), pp. 497-508 | DOI | Zbl

[Zag94] D. Zagier Values of zeta functions and their applications, First European Congress of Mathematics (Paris, July 6–10, 1992) Vol. II, Birkhäuser Basel, Basel, 1994, pp. 497-512 | DOI | Zbl

[Zud01] W. Zudilin One of the numbers $\zeta \left(5\right)$, $\zeta \left(7\right)$, $\zeta \left(9\right)$, $\zeta \left(11\right)$ is irrational, Uspehi Mat. Nauk, Volume 56 (2001) no. 4(340), pp. 149-150 | DOI | Zbl