High-low analysis and small cap decoupling over non-Archimedean local fields

Ben Johnsrude

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arXiv · 2409.09163

High-low analysis and small cap decoupling over non-Archimedean local fields

Ben Johnsrude

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Abstract

We prove a small cap decoupling theorem for the parabola over a general non-Archimedean local field for which $2\neq 0$. We obtain polylogarithmic dependence on the scale parameter $R$ and polynomial dependence in the residue prime, except for the prime 2 for which the polynomial depends on degree. Our constants are fully explicit.

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Ben Johnsrude. 2024-09-13. High-low analysis and small cap decoupling over non-Archimedean local fields. https://arxiv.org/abs/2409.09163

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