PreprintarXiv licencearXiv
Mellin Transform formulas for special values of Goss L-functions
Abstract
In the present paper, we provide formulas for the special values of dual Goss L-functions of Drinfeld modules at any non-negative integer in terms of the determinant of the values of a motivic map, extensively studied by both authors in 2026, for a large class of Anderson modules. Our result may be seen as a function field analogue of conjectural formulas for special values of motivic L-functions in terms of algebraic Mellin integrals.
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BibTeX
@misc{gezmis2026mellin,
title = {{Mellin Transform formulas for special values of Goss $L$-functions}},
author = {Oğuz Gezmiş and Nathan Green},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.09821},
eprint = {2611.09821},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.09821},
}
RIS
TY - UNPB
TI - Mellin Transform formulas for special values of Goss L-functions
AU - Oğuz Gezmiş
AU - Nathan Green
PY - 2026
DA - 2026/11/06
PB - arXiv
DO - 10.48550/arxiv.2611.09821
UR - https://arxiv.org/abs/2611.09821
AB - In the present paper, we provide formulas for the special values of dual Goss L-functions of Drinfeld modules at any non-negative integer in terms of the determinant of the values of a motivic map, extensively studied by both authors in 2026, for a large class of Anderson modules. Our result may be seen as a function field analogue of conjectural formulas for special values of motivic L-functions in terms of algebraic Mellin integrals.
ER -