On the Goncharov Depth Conjecture and polylogarithms of depth two

2022/10/21 by Steven J. Charlton, Herbert Gangl, Charlton, Steven +4
Mathematics · #Advanced Mathematical Identities #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2210.11938

openalex publication_date 2022/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the surjectivity part of Goncharov's depth conjecture. We also show that the depth conjecture implies that multiple polylogarithms of depth d and weight n can be expressed via a single function Li_{n-d+1,1,…,1}(a₁,a₂,…,a_d), and we prove this latter statement for d=2.

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