定量不发散性及具有代数坐标的点靠近流形的下界
数论
2020-08-18 v2
摘要
点计数估计是度量 Diophantine 逼近中各类结果的关键垫脚石。本文中，我们利用 Kleinbock 与 Margulis 最初发展的定量不发散估计，改进 Bernik、Götze 等人关于具有代数共轭坐标且靠近给定流形的点数的下界。在此过程中，我们也改进了关于多项式约束逼近问题的 Khinchin-Groshev 型定理。
引用
@article{arxiv.2006.10790,
title = {Quantitative non-divergence and lower bounds for points with algebraic coordinates near manifolds},
author = {Alessandro Pezzoni},
journal= {arXiv preprint arXiv:2006.10790},
year = {2020}
}
备注
Added simplified versions of the main results to the introduction -- removed some superflous hypotheses -- made explicit the last part of the argument in the "Ubiquity" section -- renamed the two main corollaries as theorems -- fixed some typos