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The Wiener-Ikehara theorem by complex analysis
Author(s):
Jaap
Korevaar
Journal:
Proc. Amer. Math. Soc.
134
(2006),
1107-1116.
MSC (2000):
Primary 40E05;
Secondary 11M45, 11N05, 44A10
Posted:
August 12, 2005
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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?
References:
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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:
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
Posted:
August 12, 2005
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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