On three notes of Stieltjes concerning Dirichlet series
type: Item
instance of: scholarly article
title: On three notes of Stieltjes concerning Dirichlet series
zbMATH Open document ID: 0877.01023
author: Jean-Pierre Kahane
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 1997-11-26T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73403
review text: The paper begins by a brief analysis of three papers of Stieltjes of 1885 and 1887 containing some mistaken proofs of the Riemann hypothesis and the prime number theorem. The author then sketches a new simple proof of Beurling's generalisation of the prime number theorem based on Fourier analysis. He also deals with some results of Stieltjes on the multiplication of Dirichlet series. Details of proofs will appear elsewhere but the historical analysis given is readable.
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 01A70
zbMATH DE Number: 1013856
reviewed by: Srishti D. Chatterji
MaRDI profile type: Publication
OpenAlex ID: W2327154305
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DOI: 10.5802/AFST.848
description: scientific article; zbMATH DE number 1013856