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Remarques sur les différentielles des polylogarithmes uniformes. (Remarks on the differentials of the uniform polylogarithms.). (French) Zbl 0861.19003
Summary: The purpose of the article is to study functional equations for the differentials of polylogarithms. One of the main ingredients is an infinitesimal analogue of a complex introduced by Goncharov [cf. A. B. Goncharov, Proc. Symp. Pure Math. 55, Pt. 2, 43-96 (1994; Zbl 0842.11043)]. As a result, one obtains a 22-term relation for the differential of the trilogarithm.

MSC:
19F27 Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects)
11R70 \(K\)-theory of global fields
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