English

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 202\neq 0. We obtain polylogarithmic dependence on the scale parameter RR 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

R2 v1 2026-06-28T18:44:17.910Z