2019/08/29 by Roswitha Hofer, Hofer, Roswitha, Lisa Kaltenböck +1
Mathematics · #Analytic Number Theory Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Number Theory (math.NT) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1908.11147
openalex publication_date 2019/08/29 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
Niederreiter and Halton sequences are two prominent classes of\nmulti-dimensional sequences which are widely used in practice for numerical\nintegration methods because of their excellent distribution qualities. In this\npaper, we show that these sequences - even though they are uniformly\ndistributed - fail to satisfy the stronger property of Poissonian pair\ncorrelations. This extends already established results for one-dimensional\nsequences and confirms a conjecture of Larcher and Stockinger. The proofs rely\non a general tool which identifies specific regularities of a sequence to be\nsufficient for not having Poissonian pair correlations.\n