Remark on a result of Bourgain on poissonian pair correlation

2017/11/23 by Gerhard Larcher, Larcher, Gerhard
Mathematics · #11K38 #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1711.08663

openalex publication_date 2017/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show for a class of sequences (a_n)_{n≥ 1} of distinct positive integers, that for no α the sequence (\a_n α\)_{n ≥ 1} does have Poissonian pair correlation. This class contains for example all strictly increasing integer sequences with positive upper density. This result motivates us to state a certain conjecture on Poissonian pair correlation which would be a significantly stronger version of a result of Jean Bourgain.

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