Advanced Studies in Pure Mathematics

Simple analytic proofs of some versions of the abstract Prime Number Theorem

Oswald Riemenschneider

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Abstract

On exactly one typewritten page, Ernst Witt sketched in the 60th of the last century a proof of the Prime Number Theorem, even in a generalized abstract situation. A closer inspection reveals a deep correlation to several other publications before and around this time. We elaborate his outline in more detail (without trying to find the "historical truth" of priority) and demonstrate that only some part of his approach can be combined with the quite recent very elegant method of Newman and Korevaar to yield a really simple analytic proof of a version of the abstract Prime Number Theorem that is close to Beurling's original one.

Article information

Source
Singularities — Niigata–Toyama 2007, J.-P. Brasselet, S. Ishii, T. Suwa and M. Vaquie, eds. (Tokyo: Mathematical Society of Japan, 2009), 249-283

Dates
Received: 21 December 2007
Revised: 8 September 2008
First available in Project Euclid: 28 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543448021

Digital Object Identifier
doi:10.2969/aspm/05610249

Mathematical Reviews number (MathSciNet)
MR2604086

Zentralblatt MATH identifier
1209.11085

Keywords
(Abstract) Prime Number Theorem Tauber Theorems Ikehara–Wiener Theorem

Citation

Riemenschneider, Oswald. Simple analytic proofs of some versions of the abstract Prime Number Theorem. Singularities — Niigata–Toyama 2007, 249--283, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05610249. https://projecteuclid.org/euclid.aspm/1543448021


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