On three notes of Stieltjes concerning Dirichlet series
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.
scientific article; zbMATH DE number 1013856
scientific article