On the finite pair correlation function of van der Corput sequences

2023/06/17 by Christian Weiß, Weiß, Christian
Physics and Astronomy · #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2306.10437

openalex publication_date 2023/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we derive an explicit formula for the finite empiric pair correlation function F_N(s) of the van der Corput sequence in base 2 for all N ∈ ℕ and s ≥ 0. The formula can be evaluated without explicit knowledge about the elements of the van der Corput sequence. Moreover, it can be immediately read off that lim_{N → ∞} F_N(s) exists only for 0 ≤ s ≤ 1/2.

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