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Beurling numbers whose number of prime factors lies in a specified residue class

Gregory Debruyne (UGent)
(2020) ACTA ARITHMETICA. 196(4). p.433-438
Author
Organization
Abstract
We find asymptotics for SK,c(x), the number of positive integers below x whose number of prime factors is c mod K. We study this question in the context of Beurling integers.
Keywords
Beurling numbers, generalized primes, Halasz theorem, residue class, number of prime factors, HALASZS THEOREM

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Citation

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MLA
Debruyne, Gregory. “Beurling Numbers Whose Number of Prime Factors Lies in a Specified Residue Class.” ACTA ARITHMETICA, vol. 196, no. 4, 2020, pp. 433–38, doi:10.4064/aa200130-15-6.
APA
Debruyne, G. (2020). Beurling numbers whose number of prime factors lies in a specified residue class. ACTA ARITHMETICA, 196(4), 433–438. https://doi.org/10.4064/aa200130-15-6
Chicago author-date
Debruyne, Gregory. 2020. “Beurling Numbers Whose Number of Prime Factors Lies in a Specified Residue Class.” ACTA ARITHMETICA 196 (4): 433–38. https://doi.org/10.4064/aa200130-15-6.
Chicago author-date (all authors)
Debruyne, Gregory. 2020. “Beurling Numbers Whose Number of Prime Factors Lies in a Specified Residue Class.” ACTA ARITHMETICA 196 (4): 433–438. doi:10.4064/aa200130-15-6.
Vancouver
1.
Debruyne G. Beurling numbers whose number of prime factors lies in a specified residue class. ACTA ARITHMETICA. 2020;196(4):433–8.
IEEE
[1]
G. Debruyne, “Beurling numbers whose number of prime factors lies in a specified residue class,” ACTA ARITHMETICA, vol. 196, no. 4, pp. 433–438, 2020.
@article{8687953,
  abstract     = {{We find asymptotics for SK,c(x), the number of positive integers below x whose number of prime factors is c mod K. We study this question in the context of Beurling integers.}},
  author       = {{Debruyne, Gregory}},
  issn         = {{0065-1036}},
  journal      = {{ACTA ARITHMETICA}},
  keywords     = {{Beurling numbers,generalized primes,Halasz theorem,residue class,number of prime factors,HALASZS THEOREM}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{433--438}},
  title        = {{Beurling numbers whose number of prime factors lies in a specified residue class}},
  url          = {{http://doi.org/10.4064/aa200130-15-6}},
  volume       = {{196}},
  year         = {{2020}},
}
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