Open Access
June 2012 A PNT equivalence for Beurling numbers
Harold G. Diamond, Wen-Bin Zhang
Funct. Approx. Comment. Math. 46(2): 225-234 (June 2012). DOI: 10.7169/facm/2012.46.2.7

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.

Citation

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Harold G. Diamond. Wen-Bin Zhang. "A PNT equivalence for Beurling numbers." Funct. Approx. Comment. Math. 46 (2) 225 - 234, June 2012. https://doi.org/10.7169/facm/2012.46.2.7

Information

Published: June 2012
First available in Project Euclid: 25 June 2012

zbMATH: 1318.11124
MathSciNet: MR2931668
Digital Object Identifier: 10.7169/facm/2012.46.2.7

Subjects:
Primary: 11N80

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

Rights: Copyright © 2012 Adam Mickiewicz University

Vol.46 • No. 2 • June 2012
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