Uniform distribution of subpolynomial functions along primes and applications

2015/03/17 by Bergelson, Vitaly, Kolesnik, Grigori, Son, Younghwan · 3 citations
#Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1503.04960

Abstract

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 ∈ H be a subpolynomial function. Let P = \2, 3, 5, 7, … \ be the (naturally ordered) set of primes. We show that (f(n))_{n ∈ ℕ} is uniformly distributed mod 1 if and only if (f(p))_{p ∈ 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].

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