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Zagier's polylogarithm conjecture revisited

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Speaker: 
Herbert Gangl
Affiliation: 
U of Durham/MPIM
Date: 
Tue, 10/03/2015 - 14:00 - 15:00
Location: 
MPIM Lecture Hall

In the early nineties, Goncharov proved the weight 3 case of Zagier's Conjecture stating that the special value $\zeta_F(3)$ of a number field $F$ is essentially expressed as a determinant of trilogarithm values taken in that field. He also envisioned a vast--partly conjectural--programme of how to approach the conjecture for higher weight. We can remove one important roadblock in weight~4 by solving one of Goncharov's conjectures. It further allows us to deduce a functional equation for $Li_4$ in four variables as one expects to enter in a more explicit definition of a certain algebraic $K$-group.

 
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