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arXiv · 2307.09403

Duality-reflection formulas of multiple polylogarithms and their $\ell$-adic Galois analogues

Densuke Shiraishi
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Abstract

In the present paper, we derive formulas of complex and $\ell$-adic multiple polylogarithms, which have two aspects: a duality in terms of indexes and a reflection in terms of variables. We provide an algebraic proof of these formulas by using algebraic relations between associators arising from the $S_3$-symmetry of the projective line minus three points.

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Densuke Shiraishi. 2023-07-18. Duality-reflection formulas of multiple polylogarithms and their $\ell$-adic Galois analogues. https://doi.org/10.18926/mjou%2F66008

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