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Uniform Distribution of Subpolynomial Functions Along Primes and Applications by Bergelson, Vitaly; Kolesnik, Grigori; Son, Younghwan is a scholarly article available to read on EtoBox.

What is Uniform Distribution of Subpolynomial Functions Along Primes and Applications about?

Let $H$ be a Hardy field (a field consisting of germs of real-valued functions at infinity that is closed under differentiation) and let $f \in H$ be a subpolynomial function. Let $\mathcal{P} = \{2, 3, 5, 7, \dots \}$ be the (naturally ordered) set of primes. We show that $(f(n))_{n \in \mathbb{N}}$ is uniformly distributed mod 1 if and only if $(f(p))_{p \in \mathcal{P}}$ is uniformly distributed mod 1. This result is then utilized to derive various ergodic and combinatorial statements which significantly generalize the results obtained in [BKMST].

Author

Bergelson, Vitaly; Kolesnik, Grigori; Son, Younghwan

Published

2015

Language

EN