The paper establishes the first criteria for the linear independence of multiple polylogarithm values over algebraic number fields via explicit Padé-type approximants, including results on products at distinct points.
V¨ a¨ an¨ anen,On linear forms of a certain class ofG-functions andp-adicG-functions, Acta Arith., 36(1980) 273–295
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Linear independence of periods related to polylogarithms
The paper establishes the first criteria for the linear independence of multiple polylogarithm values over algebraic number fields via explicit Padé-type approximants, including results on products at distinct points.