All Outputs (23)

Functional equations for higher logarithms (2003)
Journal Article
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

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... Read More about Functional equations for higher logarithms.

Quelques calculs de la cohomologie de GL_N(Z) et de la K-theorie de Z (2002)
Journal Article
Elbaz-Vincent, P., Gangl, H., & Soulé, C. (2002). Quelques calculs de la cohomologie de GL_N(Z) et de la K-theorie de Z. Comptes Rendus Mathématique, 335(4), 321-324. https://doi.org/10.1016/s1631-073x%2802%2902481-0

Voronoi cell decomposition is used to determine most of the structure of the homology of GL_N(Z) for N=5, 6. This determines K_5(Z) and gives that K_6(Z) is a 3-group.

On poly(ana)logs I (2002)
Journal Article
Elbaz-Vincent, P., & Gangl, H. (2002). On poly(ana)logs I. Compositio Mathematica, 130(2), 161-214. https://doi.org/10.1023/a%3A1013757217319

We investigate a connection between the differential of polylogarithms (as considered by Cathelineau) and a finite variant of them. This allows to answer a question raised by Kontsevich concerning the construction of functional equations for the fini... Read More about On poly(ana)logs I.