In a recent work of David, Hirata-Kohno, and Kawashima, they found an explicit sufficient condition for polylogarithms at algebraic numbers to be linearly independent over the field of rational numbers by using the Pade approximation. In this talk, we study an analogous problem in the function field setting with a different approach. More precisely, we establish some explicit sufficient conditions for the linear independence of Carlitz polylogarithms at algebraic points using the theory of Anderson dual t-motives and the detailed analysis of a specific Frobenius difference equation. This is joint work with Ryotaro Harada.

 

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