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The Wiener-Ikehara theorem by complex analysis |
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| Authors: | Jaap Korevaar |
| Institution: | KdV Institute of Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, Netherlands |
| 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? |
| Keywords: | Laplace transform prime number theorem Tauberian theory Wiener--Ikehara theorem |
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