Some conjectures and results about multizeta values for Fq[t]

In this paper, we explain several conjectures about how a product of two Carlitz–Goss zeta values can be expressed as an Fp-linear combination of Thakur's multizeta values (Thakur, 2004 [5], ), generalizing the q=2 case dealt in Thakur (2009) [6]. 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.