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arXiv · 2605.17756

Linear independence of periods related to polylogarithms

Makoto Kawashima
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Abstract

This paper provides the first criteria for the linear independence of multiple polylogarithm values over algebraic number fields. In particular, we derive novel results regarding the linear independence of products of polylogarithms at distinct points over an algebraic number field. Our approach is based on the explicit construction of Pad\'{e}-type approximants tailored for multiple polylogarithms.

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Makoto Kawashima. 2026-05-18. Linear independence of periods related to polylogarithms. https://arxiv.org/abs/2605.17756

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