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arXiv · 1311.2491

The Prime Number Theorem via Karamata's proof of the Landau-Ingham Tauberian theorem

Michael Mueger
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Abstract

This is an exposition, in 12 pages including all prerequisites and a generalization, of Karamata's little known elementary proof of the Landau-Ingham Tauberian theorem, a result in real analysis from which the Prime Number Theorem follows in a few lines. We believe this to be the most transparent of the elementary proofs of the PNT.

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Michael Mueger. 2013-11-11. The Prime Number Theorem via Karamata's proof of the Landau-Ingham Tauberian theorem. https://arxiv.org/abs/1311.2491

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