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Halász's theorem for Beurling generalized numbers

Volume 194 / 2020

Gregory Debruyne, Frederick Maes, Jasson Vindas Acta Arithmetica 194 (2020), 59-72 MSC: Primary 11N37, 11N80; Secondary 11N05, 11N64, 11M41. DOI: 10.4064/aa190210-22-5 Published online: 27 February 2020

Abstract

We show that Halász’s theorem holds for Beurling numbers under the following two mild hypotheses on the generalized number system: existence of a positive density for the generalized integers and a Chebyshev upper bound for the generalized primes.

Authors

  • Gregory DebruyneDepartment of Mathematics:
    Analysis, Logic, and Discrete Mathematics
    Ghent University
    Krijgslaan 281
    B 9000 Ghent, Belgium
    e-mail
  • Frederick MaesDepartment of Mathematics:
    Analysis, Logic, and Discrete Mathematics
    Ghent University
    Krijgslaan 281
    B 9000 Ghent, Belgium
    e-mail
  • Jasson VindasDepartment of Mathematics
    Analysis, Logic and Discrete Mathematics
    Ghent University
    Krijgslaan 281
    B 9000 Ghent, Belgium
    e-mail

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