2012/09/17 by Ingrid Carbone, Carbone, Ingrid · 3 citations
Mathematics · #11K06 #11K31 #11K38 #Analytic Number Theory Research #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Number Theory (math.NT) #math.NT #msc:11K06 #msc:11K31 #msc:11K38
paper · pdf · doi:10.48550/arxiv.1209.3611
This paper is withdrawn as it is replaced by "How to construct generalized van der Corput sequences" - arXiv:1304.5083. The latter paper coincides with the former, up to minor changes, an improvement of the references, and (hopefully) a more clear presentation. The new title would better show the aim of the paper, which has been submitted in this final form
openalex publication_date 2012/09/17 · arxiv created 2013/04/22 · arxiv updated 2013/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we associate to any LS-sequence of partitions ρL,Sn the corresponding LS-sequence of points ξL,Sn obtained reordering the points of each partition with an explicit algorithm. The procedure begins with the representation in base L+S of natural numbers, [n]L+S, and ends with the LS-radical inverse function ϕL,S, introduced ad hoc, evaluated at an appropriate subsequence of natural numbers depending on L and S. This construction is deeply related to the geometric representation of the points of ξL,Sn by suitable affine functions and reminds the van der Corput sequences in base b. Keywords: Uniform distribution, sequences of partitions, van der Corput sequences, discrepancy.