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SUMMARY:Zagier's polylogarithm conjecture on $\\zeta_F(4)$ and an explicit
  4-ratio - Steven Charlton (Universität Hamburg)
DTSTART:20220623T095500Z
DTEND:20220623T103500Z
UID:TALK174449@talks.cam.ac.uk
DESCRIPTION:In his celebrated proof of Zagier's polylogarithm conjecture f
 or 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 conject
 ure in higher weights. Recently\, Goncharov and Rudenko proved the weight 
 4 case of Zagier's conjecture with a somewhat indirect method where they a
 voided the need to define a corresponding "quadruple ratio". We propose an
  explicit candidate for such a "quadruple ratio" and as a by-product we ge
 t an explicit formula for the Borel regulator of $K_7(F)$ in terms of the 
 tetralogarithm function (joint work with H. Gangl and D. Radchenko).&nbsp\
 ;
LOCATION:Seminar Room 1\, Newton Institute
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