Linear relations among algebraic points on tensor powers of the Carlitz module

Yen-Tsung Chen, Ryotaro Harada

Published 2023-07-27Version 1

In the present paper, we study linear equations on tensor powers of the Carlitz module using the theory of Anderson dual $t$-motives and a detailed analysis of a specific Frobenius difference equation. As an application, we derive some explicit sufficient conditions for the linear independence for Carlitz polylogarithms at algebraic points in both $\infty$-adic and $v$-adic settings.