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On a Tauberian theorem of Landau


Author: Basil Gordon
Journal: Proc. Amer. Math. Soc. 9 (1958), 693-696
MSC: Primary 40.00
DOI: https://doi.org/10.1090/S0002-9939-1958-0104084-5
MathSciNet review: 0104084
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  • [1] P. L. Tschebyschef, Mémoire sur les nombres premiers, J. Math. Pures Appl. series 1, vol. 17 (1852) pp. 366-390.
  • [2] J. J. Sylvester, On Tschebyschef's theorem of the totality of prime numbers comprised within given limits, Amer. J. Math. vol. 4 (1881) pp. 230-247. MR 1505291
  • [3] E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Leipzig, 1909.
  • [4] H. N. Shapiro, On the number of primes less than or equal to $ x$, Proc. Amer. Math. Soc. vol. 1 (1950) pp. 346-348. MR 0036260 (12:80j)
  • [5] A. E. Ingham, Some Tauberian theorems connected with the prime number theorem, J. London Math. Soc. vol. 20 (1945) pp. 171-180. MR 0017392 (8:147i)
  • [6] E. Trost, Primzahlen, Basel, 1953. MR 0058630 (15:401g)
  • [7] A. Selberg, An elementary proof of the prime number theorem, Ann. of Math. vol. 50 (1949) pp. 305-313. MR 0029410 (10:595b)
  • [8] E. Landau, Über den Zusammenhang einiger neuerer Sätze der analytischen Zahlentheorie, Wiener Sitzungsberichte, Math. Klasse, vol. 115 (1906) pp. 589-632.
  • [9] P. Erdös, On a new method in elementary number theory which leads to an elementary proof of the prime number theorem, Proc. Nat. Acad. Sci. U.S.A. vol. 35 (1949) pp. 374-384. MR 0029411 (10:595c)

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DOI: https://doi.org/10.1090/S0002-9939-1958-0104084-5
Article copyright: © Copyright 1958 American Mathematical Society

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