Estimates of the Discrepancy Function in Exponential Orlicz Spaces

2013/06/07 by Gagik Amirkhanyan, Amirkhanyan, Gagik, Dmitriy Bilyk +4
Computer Science · Mathematics · #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #Digital Image Processing Techniques #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT) #math.CA #math.NT

paper · pdf · doi:10.48550/arxiv.1306.1766

13 pages

arxiv created 2013/06/07 · openalex publication_date 2013/06/07 · arxiv updated 2013/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that in all dimensions n at least 3, for every integer N there exists a distribution of points of cardinality N, for which the associated discrepancy function D_N satisfies the estimate an estimate, of sharp growth rate in N, in the exponential Orlicz class exp)L^2/(n+1). This has recently been proved by M.~Skriganov, using random digit shifts of binary digital nets, building upon the remarkable examples of W.L.~Chen and M.~Skriganov. Our approach, developed independently, complements that of Skriganov.

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