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

Yen-Tsung Chen; Ryotaro Harada

doi:10.2969/jmsj/91829182

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arXiv · 2307.14992

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

Yen-Tsung Chen·Ryotaro Harada

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Abstract

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.

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Yen-Tsung Chen, Ryotaro Harada. 2023-07-27. Linear relations among algebraic points on tensor powers of the Carlitz module. https://doi.org/10.2969/jmsj%2F91829182

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