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On l-Adic Iterated Integrals, II Functional Equations and l-Adic Polylogarithms

Published online by Cambridge University Press:  11 January 2016

Zdzislaw Wojtkowiak
Zdzislaw Wojtkowiak*
Affiliation:
Université de Nice-Sophia Antipolis, Département de Mathématiques, Laboratoire Jean Alexandre Dieudonné, U.R.A. au C.N.R.S., No 168, Parc Valrose - B.P.N° 71, 06108 Nice Cedex 2, France, wojtkow@math.unice.fr
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Abstract

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We continue to study l-adic iterated integrals introduced in the first part. We shall show that the l-adic iterated integrals satisfy essentially the same functional equations as the classical complex iterated integrals. Next we are studying l-adic analogs of classical polylogarithms.

Keywords

11G5511G9914G32

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 177 , 2005 , pp. 117 - 153
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2005

References

[B] Bourbaki, N., Eléments de mathématiques, Groupes et algebres de Lie, Diffusion C.C.L.S., Paris, 1972.Google Scholar
[BD] Beilinson, A. A. and Deligne, P., Interprétation motivique de la conjecture de Za- gier reliant polylogarithmes et régulareurs, Motives (Jannsen, U., Kleiman, S. L. and Serre, J.-P., eds.), Proc. of Symp. in Pure Math. 55, Part II, AMS (1994), pp. 97–121.Google Scholar
[Ch] Chen, K. T., Iterated integrals, fundamental groups and covering spaces, Trans. of the Amer. Math. Soc., 206 (1975), 83–98.Google Scholar
[D] Deligne, P., Le groupe fondamental de la droite projective moins trois points, Galois Groups over Q (Y. Ihara, K. Ribet and J.-P. Serre, eds.), Mathematical Sciences Research Institute Publications, no 16 (1989), pp. 79–297.Google Scholar
[I1] Ihara, Y., Profinite braid groups, Galois representations and complex multiplications, Annals of Math., 123 (1986), 43–106.Google Scholar
[I2] Ihara, Y., Braids, Galois Groups and Some Arithmetic Functions, Proc. of the Int. Cong. of Math. Kyoto (1990), 99–119.Google Scholar
[W1] Wojtkowiak, Z., The Basic Structure of Polylogarithmic Functional Equations, Structural Properties of Polylogarithms (L. Lewin, ed.), Mathematical Surveys and Monographs, Vol 37, pp. 205–231.Google Scholar