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PRIME NUMBER THEOREM EQUIVALENCES AND NON-EQUIVALENCES

Part of: Multiplicative number theory

Published online by Cambridge University Press:  29 November 2017

Harold G. Diamond  and
Wen-Bin Zhang
Harold G. Diamond
Affiliation:
Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, IL 61801, U.S.A. email diamond@math.uiuc.edu
Wen-Bin Zhang
Affiliation:
Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, IL 61801, U.S.A. email cheungmanping@yahoo.com
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Abstract

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.

MSC classification

Primary: 11N80: Generalized primes and integers
Type
Research Article
Information
Mathematika , Volume 63 , Issue 3 , 2017 , pp. 852 - 862
Copyright
Copyright © University College London 2017 

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References

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