On the algebraic independence of logarithms of Anderson $t$-modules
Number Theory
2025-04-04 v2
Abstract
In the present paper, we determine the algebraic relations among the tractable coordinates of logarithms of Anderson -modules constructed by taking the tensor product of Drinfeld modules of rank defined over the algebraic closure of the rational function field and their -st exterior powers with the Carlitz tensor powers. Our results, in the case of the tensor powers of the Carlitz module, generalize the work of Chang and Yu on the algebraic independence of polylogarithms.
Cite
@article{arxiv.2407.18916,
title = {On the algebraic independence of logarithms of Anderson $t$-modules},
author = {Oğuz Gezmiş and Changningphaabi Namoijam},
journal= {arXiv preprint arXiv:2407.18916},
year = {2025}
}
Comments
40 pages. This is the final version of the manuscript, to appear in Kyushu Journal of Mathematics