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On $$l$$-adic iterated integrals. III: Galois actions on fundamental groups. (English) Zbl 1134.11331
Summary: We continue to study $$l$$-adic iterated integrals introduced in the first part [Nagoya Math. J. 176, 113–158 (2004; Zbl 1160.11333)]. We calculate explicitly $$l$$-adic logarithm and $$l$$-adic polylogarithms. Next we use these results to study Galois representations on the fundamental group of $$\mathbb P^1_{\overline{\mathbb Q(\mu_n)}}\setminus\{0,\mu_n,\infty\}$$.
Fro Part II, see Nagoya Math. J. 177, 117–153 (2005; Zbl 1161.11363).

##### MSC:
 11G55 Polylogarithms and relations with $$K$$-theory 19D45 Higher symbols, Milnor $$K$$-theory 19D55 $$K$$-theory and homology; cyclic homology and cohomology 19E20 Relations of $$K$$-theory with cohomology theories 19F27 Étale cohomology, higher regulators, zeta and $$L$$-functions ($$K$$-theoretic aspects)
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