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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Wiener-Ikehara theorem by complex analysis


Author: Jaap Korevaar
Journal: Proc. Amer. Math. Soc. 134 (2006), 1107-1116
MSC (2000): Primary 40E05; Secondary 11M45, 11N05, 44A10
Published electronically: August 12, 2005
MathSciNet review: 2196045
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Abstract: The Tauberian theorem of Wiener and Ikehara provides the most direct way to the prime number theorem. Here it is shown how Newman's contour integration method can be adapted to establish the Wiener-Ikehara theorem. A simple special case suffices for the PNT. But what about the twin-prime problem?


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Additional Information

Jaap Korevaar
Affiliation: KdV Institute of Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, Netherlands
Email: korevaar@science.uva.nl

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08060-3
PII: S 0002-9939(05)08060-3
Keywords: Laplace transform, prime number theorem, Tauberian theory, Wiener--Ikehara theorem
Received by editor(s): April 20, 2004
Received by editor(s) in revised form: November 2, 2004
Published electronically: August 12, 2005
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.