High-low analysis and small cap decoupling over non-Archimedean local fields
Classical Analysis and ODEs
2025-09-25 v2
Abstract
We prove a small cap decoupling theorem for the parabola over a general non-Archimedean local field for which . We obtain polylogarithmic dependence on the scale parameter and polynomial dependence in the residue prime, except for the prime 2 for which the polynomial depends on degree. Our constants are fully explicit.
Keywords
Cite
@article{arxiv.2409.09163,
title = {High-low analysis and small cap decoupling over non-Archimedean local fields},
author = {Ben Johnsrude},
journal= {arXiv preprint arXiv:2409.09163},
year = {2025}
}
Comments
34 pages New version: corrects various minor errors, slightly improves numerology. Three applications are added to real-variable integrals