Linear independence of periods related to polylogarithms

TL;DR

This paper establishes new criteria for the linear independence of multiple polylogarithm values over algebraic number fields, using Padé-type approximants to derive novel results.

Contribution

It introduces the first criteria for linear independence of multiple polylogarithm values over algebraic number fields, advancing understanding in this area.

Findings

Criteria for linear independence over algebraic number fields

Results on independence of products of polylogarithms at distinct points

Construction of Padé-type approximants for multiple polylogarithms

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.