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On PNT equivalences for Beurling numbers

Gregory Debruyne (UGent) and Jasson Vindas Diaz (UGent)
(2017) MONATSHEFTE FUR MATHEMATIK. 184(3). p.401-424
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Organization
Abstract
In classical prime number theory several asymptotic relations are considered to be "equivalent" to the prime number theorem. In the setting of Beurling generalized numbers, this may no longer be the case. Under additional hypotheses on the generalized integer counting function, one can however still deduce various equivalences between the Beurling analogues of the classical PNT relations. We establish some of the equivalences under weaker conditions than were known so far.
Keywords
Beurling generalized numbers, sharp Mertens relation, prime number theorem, mean-value vanishing of the Möbius function, zeta functions, Landau relations, PNT equivalences, PRIME-NUMBERS, THEOREM

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Please use this url to cite or link to this publication:

MLA
Debruyne, Gregory, and Jasson Vindas Diaz. “On PNT Equivalences for Beurling Numbers.” MONATSHEFTE FUR MATHEMATIK 184.3 (2017): 401–424. Print.
APA
Debruyne, G., & Vindas Diaz, J. (2017). On PNT equivalences for Beurling numbers. MONATSHEFTE FUR MATHEMATIK, 184(3), 401–424.
Chicago author-date
Debruyne, Gregory, and Jasson Vindas Diaz. 2017. “On PNT Equivalences for Beurling Numbers.” Monatshefte Fur Mathematik 184 (3): 401–424.
Chicago author-date (all authors)
Debruyne, Gregory, and Jasson Vindas Diaz. 2017. “On PNT Equivalences for Beurling Numbers.” Monatshefte Fur Mathematik 184 (3): 401–424.
Vancouver
1.
Debruyne G, Vindas Diaz J. On PNT equivalences for Beurling numbers. MONATSHEFTE FUR MATHEMATIK. 2017;184(3):401–24.
IEEE
[1]
G. Debruyne and J. Vindas Diaz, “On PNT equivalences for Beurling numbers,” MONATSHEFTE FUR MATHEMATIK, vol. 184, no. 3, pp. 401–424, 2017.
@article{8533608,
  abstract     = {{In classical prime number theory several asymptotic relations are considered to be "equivalent" to the prime number theorem. In the setting of Beurling generalized numbers, this may no longer be the case. Under additional hypotheses on the generalized integer counting function, one can however still deduce various equivalences between the Beurling analogues of the classical PNT relations. We establish some of the equivalences under weaker  conditions than were known so far.}},
  author       = {{Debruyne, Gregory and Vindas Diaz, Jasson}},
  issn         = {{0026-9255}},
  journal      = {{MONATSHEFTE FUR MATHEMATIK}},
  keywords     = {{Beurling generalized numbers,sharp Mertens relation,prime number theorem,mean-value vanishing of the Möbius function,zeta functions,Landau relations,PNT equivalences,PRIME-NUMBERS,THEOREM}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{401--424}},
  title        = {{On PNT equivalences for Beurling numbers}},
  url          = {{http://dx.doi.org/10.1007/s00605-016-0979-9}},
  volume       = {{184}},
  year         = {{2017}},
}

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