Functiones et Approximatio Commentarii Mathematici

A PNT equivalence for Beurling numbers

Harold G. Diamond and Wen-Bin Zhang

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Abstract

In classical prime number theory, several relations are considered to be equivalent to the Prime Number Theorem. For Beurling generalized numbers, some auxiliary conditions may be needed to deduce one relation from another one. We show conditions under which the Beurling analog of the sharp version of Mertens' sum formula does or does not hold.

Article information

Source
Funct. Approx. Comment. Math., Volume 46, Number 2 (2012), 225-234.

Dates
First available in Project Euclid: 25 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.facm/1340628404

Digital Object Identifier
doi:10.7169/facm/2012.46.2.7

Mathematical Reviews number (MathSciNet)
MR2931668

Zentralblatt MATH identifier
1318.11124

Subjects
Primary: 11N80: Generalized primes and integers

Keywords
Beurling generalized numbers sharp Mertens formula Prime Number Theorem equivalent relations

Citation

Diamond, Harold G.; Zhang, Wen-Bin. A PNT equivalence for Beurling numbers. Funct. Approx. Comment. Math. 46 (2012), no. 2, 225--234. doi:10.7169/facm/2012.46.2.7. https://projecteuclid.org/euclid.facm/1340628404


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References

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