A t-motivic interpretation of shuffle relations for multizeta values

Abstract

Thakur [Tha10] showed that, for r, s∈N, a product of two Carlitz zeta values ζA(r) and ζA(s) can be expressed as an Fp-linear combination of ζA(r+s) and double zeta values of weight r+s. Such an expression is called shuffle relation by Thakur. Fixing r, s∈N, we construct a t-module E′. To determine whether an (r+s)-tuple C in Fq(θ)r+s gives a shuffle relation, we relate it to the Fq[t]-torsion property of the point vC∈E′(Fq[θ]) constructed with respect to the given (r+s)-tuple C. We also provide an effective criterion for deciding the Fq[t]-torsion property of the point vC.