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On three notes of Stieltjes concerning Dirichlet series. (Sur trois notes de Stieltjes relative aux séries de Dirichlet.) (French) Zbl 0877.01023
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.

MSC:
01A55 History of mathematics in the 19th century
01A70 Biographies, obituaries, personalia, bibliographies
Biographic References:
Stieltjes, Thomas Jean
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