This article is cited in 17 papers

Identities for Generalized Polylogarithms

E. A. Ulanskii

M. V. Lomonosov Moscow State University

Abstract: We study the behavior of generalized polylogarithms under the action of the group of fractional-linear transformations of the argument. This group is formed by the transformations $z\mapsto1-z$ and $z\mapsto-z/(1-z)$, the last of which allows us to obtain identities of the form
$$ \operatorname{Li}_k\biggl(\frac{-z}{1-z}\biggr) =-\sum_{|\bar s|=k}\operatorname{Li}_{\bar s}(z). $$
We prove that these identities imply the linear independence of generalized polylogarithms and the algebraic independence of classical polylogarithms over the field $\mathbb C(z)$.

UDC: 517.5

Received: 19.02.2002
Revised: 24.07.2002

DOI: 10.4213/mzm209

 English version: Mathematical Notes, 2003, 73:4, 571–581

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