Metric uniform distribution on analytic curves

2025/09/08 by Vitaly Bergelson, Bergelson, Vitaly, Joel Moreira +1
Mathematics · #Functional Equations Stability Results #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2509.06909

Abstract

We obtain multidimensional metric uniform distribution results involving sequences in \mathbb 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 a₁,…,a_k:\mathbb N→\mathbb Z the set \(x₁,…,x_k)∈\mathbb R^k:(a₁(n)x₁,…,a_k(n)x_k)_n∈\mathbb N is uniformly distributed in \mathbb T^k\ has full Lebesgue measure inside any non-degenerate analytic curve γ⊂\mathbb R^k.

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