Sur la conjecture de Zagier pour n=4

2008/09/23 by Nicusor Dan, Dan, Nicusor · 2 citations
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT) #math.KT #math.NT #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0809.3984

arxiv created 2008/09/23 · openalex publication_date 2008/09/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• A review of Dan's reduction method for multiple polylogarithms
• Motivic correlators, cluster varieties and Zagier's conjecture on\n zeta(F,4)

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