Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
MULTIZETA VALUES FOR Fq[t], THEIR PERIOD INTERPRETATION AND RELATIONS BETWEEN THEM
 

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 Carlitz-Tate t-motives). 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
Grothendieck-Ihara 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,

  

Source: Anderson, Greg W. - School of Mathematics, University of Minnesota

 

Collections: Mathematics