Motivic Mellin transforms
Algebraic Geometry
2024-12-24 v1 Logic
Number Theory
Abstract
This work brings Mellin transforms into the realm of motivic integration. The new, larger class of motivic functions is stable under motivic Mellin and Fourier transforms, with general Fubini results and change of variables formulas. It specializes to -adic integrals and -adic Mellin transforms uniformly in , with transfer principles between zero and positive characteristic local fields. In particular, it generalizes previous set-ups of motivic integration with Fubini from among others [16, 17, 18, 29, 9] and simplifies some aspects on the way by using the ideas of [10].
Keywords
Cite
@article{arxiv.2412.17764,
title = {Motivic Mellin transforms},
author = {Raf Cluckers and François Loeser and Kien Huu Nguyen and Floris Vermeulen},
journal= {arXiv preprint arXiv:2412.17764},
year = {2024}
}