### An explicit quadruple ratio

Heilbronn Number Theory Seminar

5th February 2020, 4:00 pm – 5:00 pm

Fry Building, 2.04

In his celebrated proof of Zagier's polylogarithm conjecture for weight 3 Goncharov introduced a "triple ratio", a projective

invariant akin to the classical cross-ratio. He has also conjectured the existence of "higher ratios" that should play an important role for Zagier's conjecture in higher weights. Recently, Goncharov and Rudenko proved the weight 4 case of Zagier's conjecture with a somewhat indirect method where they avoided the need to define a corresponding "quadruple ratio". We propose an explicit candidate for such "quadruple ratio" and as a by-product we get an explicit formula for the Borel regulator of K_7 in terms of the tetralogarithm function (joint work with H. Gangl and D. Radchenko).

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