Algebraic independence results for colored multizeta values in characteristic p

Abstract

This paper studies multizeta values in positive characteristic, which are function field analogs of the Euler–Riemann multizeta values. The objective of this paper is two-fold. We first define mixed Carlitz motives, which is a counterpart to mixed Tate motives in characteristic zero. After that, we identify special mixed Carlitz motives, and use them to derive algebraic independence properties of colored multizeta values. Our results generalize those in the literature on algebraic relations between multizeta values.