Oğuz Gezmiş, Changningphaabi Namoijam
Published 2024-07-06Version 1
In the present paper, we determine the algebraic relations among the tractable coordinates of logarithms of Anderson $t$-modules constructed by taking the tensor product of Drinfeld modules of rank $r$ defined over the algebraic closure of the rational function field and their $(r-1)$-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.
Comments: 38 pages. The work in v2 of arXiv:2110.02569 has been divided into two works, one of which is this. This paper includes generalizations of the results in section 4, section 5, and the appendix of v2 of arXiv:2110.02569
Prolongations of t-motives and algebraic independence of periods
On algebraic independence of certain multizeta values in characteristic p
Algebraic independence of the Carlitz period and the positive characteristic multizeta values at n and (n,n)
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