Functional equations for higher logarithms

Gangl, H.

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• Peer Reviewed: Not Peer Reviewed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.