Derivation and double shuffle relations for multiple zeta values

Compositio Mathematica

Volumn 142, Issue 2, 2006, Pages 307-338

  Ihara, Kentaro ^a   Kaneko, Masanobu ^b   Zagier, Don ^c,d  

^a NAGOYA UNIVERSITY   (Japan)

^b KYUSHU UNIVERSITY   (Japan)

^c MAX PLANCK INSTITUT FÜR MATHEMATIK   (Germany)

^d Centre de Recherche Interdisciplinaire en Biologie   (France)

Author keywords

Derivation; Double shuffle relation; Multiple zeta value; Regularization

Indexed keywords

EID: 33845547431     PISSN: 0010437X     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0010437X0500182X     Document Type: Article

References (21)

1. Bou00 L. Boutet de Monvel, Remarques sur les séries logarithmiques divergentes, in Polylogarithmes et conjecture de Deligne-Ihara, Luminy, April 2000 (CIRM, Marseille, 2000).
2. BK97 D. J. Broadhurst and D. Kreimer, Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops, Phys. Lett. B 393 (1997), 403-412.
3. CM04a A. Connes and H. Moscovici, Modular Hecke algebras and their Hopf symmetry, Mosc. Math. J. 4 (2004), 67-109.
4. CM04b A. Connes and H. Moscovici, Rankin-Cohen brackets and the Hopf algebra of transverse geometry, Mosc. Math. J. 4 (2004), 111-130.
5. Dri90 V. G. Drinfel'd, On quasitriangular quasi-Hopf algebras and on a group that is closely connected with Gal(ℚ/ℚ), Algebra i Analiz 2 (1990), 149-181 (in Russian).
6. (English translation in Leningrad Math. J. 2(4) (1991), 829-860).
7. N)), Duke Math. J. 110 (2001), 397-487.
8. Gon01b A. B. Goncharov, Multiple ζ-values, Galois groups and geometry of modular varieties, Progr. Math. 201 (2001), 361-392.
9. Gon01c A. B. Goncharov, Multiple polylogarithms and mixed Tate motives, Preprint (2001), math.AG/0103059.
10. Gra97 A. Granville, A decomposition of Riemann's zeta-function, in Analytic number theory, London Mathematical Society Lecture Note Series, vol. 247 (Cambridge University Press, Cambridge 1997), 95-101.
11. Hof92 M. Hoffman, Multiple harmonic series, Pacific J. Math. 152 (1992), 275-290.
12. Hof97 M. Hoffman, The algebra of multiple harmonic series, J. Algebra 194 (1997), 477-495.
13. HO03 M. Hoffman and Y. Ohno, Relations of multiple zeta values and their algebraic expression, J. Algebra 262 (2003), 332-347.
14. MPH00 H. N. Minh, M. Petitot and J. V. D. Hoeven, Shuffle algebra and polylogarithms, Discrete Math. 225 (2000), 217-230.
15. Ohn99 Y. Ohno, A generalization of the duality and sum formulas on the multiple zeta values, J. Number Theory 74 (1999), 39-43.
16. Rac02 G. Racinet, Doubles mélanges des polylogarithmes multiples aux racines de l'unité, Publ. Math. Inst. Hautes Études Sci. 95 (2002), 185-231.
17. Reu93 C. Reutenauer, Free Lie algebras (Oxford Science Publications, Oxford, 1993).
18. Ter02 T. Terasoma, Mixed Tate motives and multiple zeta values, Invent. Math. 149 (2002), 339-369.
19. Tsu04 H. Tsumura, Combinatorial relations for Euler-Zagier sums, Acta Arith. 111 (2004), 27-42.
20. Zag93 D. Zagier, Periods of modular forms, trace of Hecke operators, and multiple zeta values, RIMS Kokyuroku 843 (1993), 162-170.
21. Zag94 D. Zagier, Values of zeta functions and their applications, in First European Congress of Mathematics, Vol. II, Progr. Math. 120 (1994),497-512.