PRIME NUMBER THEOREM EQUIVALENCES AND NON-EQUIVALENCES

PRIME NUMBER THEOREM EQUIVALENCES AND NON-EQUIVALENCES

There are several formulas in classical prime number theory that are said to be “equivalent” to the Prime Number Theorem. For Beurling generalized numbers, not all such implications hold unconditionally. Here we investigate conditions under which the Beurling version of these relations do or do not...

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Veröffentlicht in:Mathematika 2017, Vol.63 (3), p.852-862
Hauptverfasser: Diamond, Harold G., Zhang, Wen-Bin
Format: Artikel
Sprache:eng
Schlagworte:
11N80 (primary)
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:There are several formulas in classical prime number theory that are said to be “equivalent” to the Prime Number Theorem. For Beurling generalized numbers, not all such implications hold unconditionally. Here we investigate conditions under which the Beurling version of these relations do or do not hold.
ISSN:0025-5793
2041-7942
DOI:10.1112/S0025579317000201