Colored multizeta values in positive characteristic

Abstract

In 2004, Thakur introduced a positive characteristic analogue of multizeta values. Later, in 2017, he mentioned the two colored variants which are positive characteristic analogues of colored multizeta values in his survey of multizeta values in positive characteristic. In this paper, we study one of those two variants. We establish their fundamental properties, that include their non-vanishing, sum-shuffle relations, 𝑡-motivic interpretation and linear independence. For the linear independence results, we prove that there are no nontrivial k ̄ \overline{k} -linear relations among the colored multizeta values with different weights.