非阿基米德局部场上的高低分析和小上限解耦

arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-09-13 DOI:arxiv-2409.09163

Ben Johnsrude

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引用次数: 0

摘要

我们证明了一个一般非阿基米德局部域上抛物线的小上限解耦定理，其中$2\neq 0$。我们得到了对尺度参数 $R$ 的多对数依赖性和对残差素数的多项式依赖性，除了素数 2 的多项式依赖于度数。我们的常数是完全明确的。

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

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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arXiv - MATH - Classical Analysis and ODEs

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