摘要
For each integer n≥2n≥2, we study linear relations among weight nn double zeta values and the nnth power of the Carlitz period over the rational function field Fq(θ)Fq(θ). We show that all the Fq(θ)Fq(θ)-linear relations are induced from the Fq[t])Fq[t])-linear relations among certain explicitly constructed special points in the nnth tensor power of the Carlitz module. We then establish a principle of Siegel’s lemma for computing and determining the Fq[t])Fq[t])-linear relations mentioned above, and thus obtain an effective criterion for computing the dimension of weight nn double zeta values space.