Linear independence of periods related to 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 Padé-type approximants tailored for multiple polylogarithms.

arXiv comment29 pages