A PNT equivalence for Beurling numbers

• DOI: 10.7169/facm/2012.46.2.7
• Publication Date: 2012-06-25T15:20:34Z
• Authors: Harold G. Diamond; Wen-Bin Zhang
• Keywords: Equivalence relation; Logical equivalence

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