Metric uniform distribution on analytic curves: With an Appendix by Jim Wright.

IF 1.2 3区数学 Q1 MATHEMATICS

Research in the Mathematical Sciences Pub Date : 2026-01-01 Epub Date: 2026-09-15 DOI:10.1007/s40687-026-00647-6

Vitaly Bergelson, Joel Moreira

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引用次数: 0

Abstract

We obtain multidimensional metric uniform distribution results involving sequences in $R^{k}$ parametrized by analytic curves. Our theorems extend the classical theorems of Weyl and Koksma in a variety of ways. One of our main results implies that for any injective sequences $a_{1}, \dots, a_{k} : N \to Z$ the set $\begin{matrix} {(x_{1}, \dots, x_{k}) \in R^{k} : (a_{1} (n) x_{1}, \dots, a_{k} (n) x_{k})_{n \in N} is uniformly distributed in T^{k}} \end{matrix}$ has full Lebesgue measure inside any non-degenerate analytic curve $γ \subset R^{k}$ .

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解析曲线上的度量均匀分布：附吉姆·赖特的附录。

得到了用解析曲线参数化的rk序列的多维度量均匀分布结果。我们的定理以各种方式扩展了Weyl和Koksma的经典定理。我们的一个主要结果意味着任何单射序列1⋯,凯西:N→Z { ( x 1⋯x k)∈R k: (1 (n) x 1⋯k (n) x k) n∈n是均匀分布在T k } 里面有完整的勒贝格测度任何简分析曲线γ⊂R k。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Research in the Mathematical Sciences Mathematics-Computational Mathematics

CiteScore

2.00

自引率

8.30%

发文量

期刊介绍： Research in the Mathematical Sciences is an international, peer-reviewed hybrid journal covering the full scope of Theoretical Mathematics, Applied Mathematics, and Theoretical Computer Science. The Mission of the Journal is to publish high-quality original articles that make a significant contribution to the research areas of both theoretical and applied mathematics and theoretical computer science. This journal is an efficient enterprise where the editors play a central role in soliciting the best research papers, and where editorial decisions are reached in a timely fashion. Research in the Mathematical Sciences does not have a length restriction and encourages the submission of longer articles in which more complex and detailed analysis and proofing of theorems is required. It also publishes shorter research communications (Letters) covering nascent research in some of the hottest areas of mathematical research. This journal will publish the highest quality papers in all of the traditional areas of applied and theoretical areas of mathematics and computer science, and it will actively seek to publish seminal papers in the most emerging and interdisciplinary areas in all of the mathematical sciences. Research in the Mathematical Sciences wishes to lead the way by promoting the highest quality research of this type.