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Functional equations for higher logarithms

Gangl, H.

Authors



Abstract

Following earlier work by Abel and others, Kummer gave in 1840 functional equations for the polylogarithm function Li_m(z) up to m = 5, but no example for larger m was known until recently. We give the first genuine 2-variable functional equation for the 7-logarithm. We investigate and relate identities for the 3-logarithm given by Goncharov and Wojtkowiak and deduce a certain family of functional equations for the 4-logarithm.

Citation

Gangl, H. (2003). Functional equations for higher logarithms. Selecta Mathematica (New Series), 9(3), 361 - 377. https://doi.org/10.1007/s00029-003-0312-z

Journal Article Type Article
Publication Date 2003-09
Deposit Date Feb 15, 2008
Journal Selecta Mathematica (New Series)
Print ISSN 1022-1824
Electronic ISSN 1420-9020
Publisher Springer
Peer Reviewed Not Peer Reviewed
Volume 9
Issue 3
Pages 361 - 377
DOI https://doi.org/10.1007/s00029-003-0312-z
Keywords Polylogarithms, Functional equations, Algebraic K-theory.

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