Year: 2025
Type: article
Abstract: We introduce formulas for the logarithms of Drinfeld modules using a framework recently developed by the second author. We write the logarithm function as the evaluation under a motivic map of a product of rigid analytic trivializations of $t$-motives. We then specialize our formulas to express special values of Goss $L$-functions as Drinfeld periods multiplied by rigid analytic trivializations evaluated under this motivic map. We view these formulas as characteristic-$p$ analogues of integral representations of Hasse–Weil-type zeta functions. We also apply this machinery for Drinfeld modules tensored with the tensor powers of the Carlitz module, which serves as the Tate twist of a Drinfeld module.
DOI: 10.1093/imrn/rnaf343
Authors: Oğuz Gezmiş, Nathan Green
Institutions: National Tsing Hua University, Louisiana Tech University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416487545