2024/12/23 by Raf Cluckers, François Loeser, Cluckers, Raf +5
Materials Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Liquid Crystal Research Advancements #Logic (math.LO) #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2412.17764
openalex publication_date 2024/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 p-adic integrals and p-adic Mellin transforms uniformly in p, 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].