Some conjectures and results about multizeta values for F_q[t]
arXiv:1108.4722 · doi:10.1016/j.jnt.2009.08.001
Abstract
In this paper, we explain several conjectures about how a product of two Carlitz-Goss zeta values can be expressed as a F_p-linear combination of Thakur's multizeta values, generalizing the q=2 case dealt by D. Thakur in Relations between multizeta values for F_q[t]. In contrast to the classical sum shuffle, ζ(a)ζ(b)=ζ(a+b)+ζ(a,b)+ζ(b,a), the identities we get are much more involved. Hundreds of instances of these conjectures have been proved and we describe the proof method and the evidence.
10 pages