A simpler normal number construction for simple Luroth series

2013/11/19 by Joseph Vandehey, Vandehey, Joseph
Mathematics · #11K16 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.NT #msc:11K16

paper · pdf · doi:10.48550/arxiv.1311.4784

arxiv created 2013/11/19 · openalex publication_date 2013/11/19 · arxiv updated 2013/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Champernowne famously proved that the number 0.(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)... formed by concatenating all the integers one after another is normal base 10. We give a generalization of Champernowne's construction to various other digit systems, including generalized Lüroth series with a finite number of digits. For these systems, our construction simplifies a recent construction given by Madritsch and Mance. Along the way we give an estimation of the sum of multinomial coefficients above a tilted hyperplane in Pascal's simplex, which may be of general interest.

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