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Multiplicative complements I

Volume 207 / 2023

Anett Kocsis, Dávid Matolcsi, Csaba Sándor, György Tőtős Acta Arithmetica 207 (2023), 101-120 MSC: Primary 11N25; Secondary 11B34. DOI: 10.4064/aa220408-3-1 Published online: 28 February 2023

Abstract

We study how dense a multiplicative basis of order $h$ for $\mathbb Z^+$ can be, improving on earlier results. Upon introducing the notion of a multiplicative complement, we present some tight density bounds.

Authors

  • Anett KocsisEötvös Loránd University
    H-1111 Budapest, Hungary
    e-mail
  • Dávid MatolcsiEötvös Loránd University
    H-1111 Budapest, Hungary
    e-mail
  • Csaba SándorDepartment of Stochastics
    Institute of Mathematics
    Budapest University of Technology and Economics
    H-1111 Budapest, Hungary
    and
    Department of Computer Science and
    Information Theory
    Budapest University of Technology and Economics
    H-1111 Budapest, Hungary
    and
    MTA-BME Lendület
    Arithmetic Combinatorics Research Group, ELKH
    H-1111 Budapest, Hungary
    e-mail
  • György TőtősFaculty of Mathematics and
    Computer Science
    Babeş-Bolyai University
    Cluj-Napoca 400157, Romania
    e-mail

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