Linear relations among double zeta values in positive characteristic Dedicated to the memory of my father

摘要

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