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References

  1. To P. L. Tschebycheff for his two papers Sur la fonction qui détermine la totalité des nombres premiers inferieurs à une limite donnée Journal de Math., 17(1), 1852, 341–365

    Google Scholar 

  2. Mémoire sur les nombres premiers,Journal de Math., 17(1), 1852, 366–390.

    Google Scholar 

  3. To Bernhard Riemann for his paper Über die Anzahl der Primzahlen unter einer gegebenen Grösse, Monatsberichte der Königlichen Preussischen Akademie der Wissenschaften zu Berlin aus dem Jahre 1859 (1860), 671–680.

    Google Scholar 

  4. To Jacques Hadamard for his two papers Étude sur les propriétés des fonctions entières et en particulier d’une fonction considérée par Riemann, Journal de Math., 9(4), 1893, 171–215

    Google Scholar 

  5. Sur la distribution des zéros de la fonction 5(s) et ses conséquences arithmétiques, Bulletin de la Soc. Math. de France, 24, 1896, 199–220.

    Google Scholar 

  6. To C.-J. de la Vallée Poussin for his two papers Recherches analytiques sur la théorie des nombres; Premiere partie: La fonction ÿ(s) de Riemann et les nombres premiers en general,Annales de la Soc. Scientifique de Bruxelles, 20, 1896, 183–256

    Google Scholar 

  7. Sur la fonction V(s) de Riemann et le nombre des nombres premiers inférieurs à une limite donnée,Mémoires couronnés et autres memoires publiés par l’Acad. Roy. des Sciences, des Lettres et des Beaux-Arts de Belgique, 59, No. 1, 1899–1900, 74 pages.

    Google Scholar 

  8. To Edmund Landau for his paper Neuer Beweis des Primzahlsatzes und Beweis des Primidealsatzes,Mathematische Annalen, 56, 1903, 645–670 in his book Handbuch der Lehre von der Verteilung der Primzahlen,Teubner, Leipzig, 1909.

    Google Scholar 

  9. To G. H. Hardy and J. E. Littlewood for their many contributions to analysis and number theory, in particular their two papers New proofs of the prime-number theorem and similar theorems, Quarterly Journal of Math., 46, 1915, 215–219

    Google Scholar 

  10. Contributions to the theory of the Riemann zeta function and the theory of the distribution of primes, Acta Math,41, 1918, 119–196.

    Google Scholar 

  11. To Norbert Wiener for his memoir Tauberian theorems,Annals of Mathematics, 33(2), 1932, 1–100.

    Google Scholar 

  12. To I. M. Vinogradov for his papers on exponential sums, particularly the three papers: On Weyl’s sums, Mat. Sbornik, 42, 1935, 521–530;

    Google Scholar 

  13. A new method of resolving certain general questions of the theory of numbers,Mat. Sbornik, 43(1), 1936, 9–19;

    Google Scholar 

  14. A new method of estimation of trigonometrical sums,Mat. Sbornik, 43(1), 1936, 175–188.

    Google Scholar 

  15. To Arne Beurling for his paper Analyse de la loi asymptotique de la distribution des nombres premiers généralisés, I,Acta Math., 68, 1937, 255–291.

    Google Scholar 

  16. To Atle Selberg for his many contributions to the theory of the zeta function and the distribution of primes and in particular for his paper, An elementary proof of the prime number theorem,Annals of Mathematics, 50(2), 1949, 305–313.

    Google Scholar 

  17. To Paul Erdös for his many papers in the theory of numbers, and in particular for his paper, On a new method in elementary number theory which leads to an elementary proof of the prime number theorem,Proceedings of the National Academy of Sciences, 35, 1949, 374–385.

    Google Scholar 

  18. BATEMAN, P.T. BASHO Major figures in the history of the prime number theorem. Abstracts Amer. Math. Soc. (87th annual meeting, San Francisco), 1981, p. 2.

    Google Scholar 

  19. BASHŌ, Narrow Road to a Far Province. Translated by Dorothy Britton. Kodanshu Publ., Tokyo, 1974.

    Google Scholar 

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© 1989 Springer-Verlag New York Inc.

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Ribenboim, P. (1989). Conclusion. In: The Book of Prime Number Records. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0507-1_8

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  • DOI: https://doi.org/10.1007/978-1-4684-0507-1_8

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