The Wiener–Ikehara theorem by complex analysis
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- by Jaap Korevaar PDF
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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
- 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
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 1107-1116
- MSC (2000): Primary 40E05; Secondary 11M45, 11N05, 44A10
- DOI: https://doi.org/10.1090/S0002-9939-05-08060-3
- MathSciNet review: 2196045