 
Summary: MULTIZETA VALUES FOR Fq[t], THEIR PERIOD
INTERPRETATION AND RELATIONS BETWEEN THEM
GREG W. ANDERSON AND DINESH S. THAKUR
Abstract. We provide a period interpretation for multizeta values (in the
function field context) in terms of explicit iterated extensions of tensor pow
ers of Carlitz motives (mixed CarlitzTate tmotives). We give examples of
combinatorially involved relations that these multizeta values satisfy.
0. Introduction
The multizeta values introduced and studied originally by Euler have been pur
sued again recently with renewed interest because of their emergence in studies in
mathematics and mathematical physics connecting diverse viewpoints. They occur
naturally as coefficients of the Drinfeld associator, and thus have connections to
quantum groups, knot invariants and mathematical physics. They also occur in the
GrothendieckIhara program to study the absolute Galois group through the funda
mental group of the projective line minus three points and related studies of iterated
extensions of Tate motives, Feynman path integral renormalizations, etc. We re
fer the reader to papers on this subject by Broadhurst, Cartier, Deligne, Drinfeld,
ŽEcalle, Furusho, Goncharov, Hoffman, Kreimer, Racinet, Terasoma, Waldschmidt,
Zagier, Zudilin to mention just a few names.
Having learned about these rich interconnections at the Arizona Winter school,
