Well-distribution of Polynomial maps on locally compact groups

2022/10/04 by Tom Meyerovitch, Meyerovitch, Tom
Mathematics · #37A44 #37A46 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2210.01429

openalex publication_date 2022/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Weyl's classical equidistribution theorem states that real-valued polynomial sequences are uniformly distributed modulo 1, unless all non-constant coefficients are rational. A continuous function between two topological groups is called a polynomial map of degree at most d if it vanishes under any d+1 difference operators. Leibman, and subsequently Green and Tao, formulated and proved equidistribution theorems about polynomial sequences that take values in a nilmanifold. We formulate and prove some general equidistribution theorems regarding polynomial maps from a locally compact group into a compact abelian group.

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