The Wiener–Ikehara theorem by complex analysis

Korevaar, Jaap

doi:10.1090/S0002-9939-05-08060-3

The Wiener–Ikehara theorem by complex analysis
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Proc. Amer. Math. Soc. 134 (2006), 1107-1116 Request permission

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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