Gangl, H. (2003) 'Functional equations for higher logarithms.', Selecta mathematica., 9 (3). 361 - 377.
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.
|Keywords:||Polylogarithms, Functional equations, Algebraic K-theory.|
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|Publisher Web site:||http://dx.doi.org/10.1007/s00029-003-0312-z|
|Record Created:||15 Feb 2008|
|Last Modified:||08 Apr 2009 16:30|
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