Some conjectures and results about multizeta values for Fq[t]
Abstract
In this paper, we explain several conjectures about how a product of two Carlitz-Goss zeta values can be expressed as a Fp-linear combination of Thakur's multizeta values, generalizing the q=2 case dealt by D. Thakur in Relations between multizeta values for Fq[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.
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