Functional equations of polygonal type for multiple polylogarithms in weights 5, 6 and 7

Steven Charlton; Herbert Gangl; Danylo Radchenko

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arXiv · 2012.09840

Functional equations of polygonal type for multiple polylogarithms in weights 5, 6 and 7

Steven Charlton·Herbert Gangl·Danylo Radchenko

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Abstract

We present new functional equations in weights 5, 6 and 7 and use them for explicit depth reduction of multiple polylogarithms. These identities generalize the crucial identity $\mathbf{Q}_4$ from the recent work of Goncharov and Rudenko that was used in their proof of the weight 4 case of Zagier's Polylogarithm Conjecture.

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Steven Charlton, Herbert Gangl, Danylo Radchenko. 2020-12-17. Functional equations of polygonal type for multiple polylogarithms in weights 5, 6 and 7. https://arxiv.org/abs/2012.09840

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