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An elementary Tauberian theorem and the prime number theorem

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References

  1. S. A. Amitsur, On arithmetic functions,J. Analyse Math.,5 (1956–57), 273–314.

    Google Scholar 

  2. E. Bombieri, Sulle formule di Selberg generalizate per classi di funzioni arithmetiche e le applicazioni al problema del resto nel “Primzahlsatz”,Riv. Mat. Univ. Parma,3 (1962), 393–440.

    Google Scholar 

  3. H. Diamond, J. Steinig, An elementary proof of the prime number theorem with a remainder term,Invent. Math.,11 (1970), 199–258.

    Google Scholar 

  4. B. Gordon, On a Tauberian theorem of Landau,Proc. Amer. Math. Soc.,9 (1958), 693–696.

    Google Scholar 

  5. P. Erdős, A. E. Ingham, Arithmetical Tauberian theorems,Acta Arithmetica,IX (1964), 341–356.

    Google Scholar 

  6. G. H. Hardy, E. M. Wright,An introduction to the theory of numbers, (Oxford, 1960).

  7. A. E. Ingham, Some Tauberian theorems connected with the prime number theorem,J. London Math. Soc.,20 (1945), 171–180.

    Google Scholar 

  8. E. Landau,Handbuch der Lehre von der Verteilung der Primzahlen (Leipzig und Berlin, 1909); Über einige neuere Grenzwertsätze,Rend. Circ. Mat. Palermo,34 (1912), 121–131.

  9. A. Selberg, An elementary proof of the prime number theorem,Annals of Math.,50 (1949), 305–314.

    Google Scholar 

  10. H. N. Shapiro, On a theorem of Selberg and generalizations,Annals of Math.,51 (1950), 485–497.

    Google Scholar 

  11. A. Walfisz,Weylsche Exponentialsummen in der neuren Zahlentheorie (Berlin, 1963).

  12. E. Wirsing, Elementare Beweise der Primzahlsatzes mit Restglied,J. Reine Angew. Math.,211 (1962), 205–214 and214/215 (1964), 1–18.

    Google Scholar 

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Balog, A. An elementary Tauberian theorem and the prime number theorem. Acta Mathematica Academiae Scientiarum Hungaricae 37, 285–299 (1981). https://doi.org/10.1007/BF01904891

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