Sur la conjecture de Zagier pour n=4

Abstract

We express a general 4-hyperlogarithm as a linear combination of 4-hyperlogarithms in two variables. We reduce the Zagier's conjecture for $n=4$ to a combinatorial statement. We give a short survey of the strategy of Goncharov and Zagier for reducing the Zagier's conjecture for general $n$ to combinatorial relations between hyperlogarithms. Such a survey is missing in the literature.

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• Progrès récents sur la conjecture de Zagier et le programme de Goncharov [d'après Goncharov, Rudenko, Gangl, ...]