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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References | Similar Articles | Additional Information
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- [3] E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Leipzig, 1909.
- [4] Harold N. Shapiro, On the number of primes less than or equal 𝑥, Proc. Amer. Math. Soc. 1 (1950), 346–348. MR 36260, https://doi.org/10.1090/S0002-9939-1950-0036260-7
- [5] A. E. Ingham, Some Tauberian theorems connected with the prime number theorem, J. London Math. Soc. 20 (1945), 171–180. MR 17392, https://doi.org/10.1112/jlms/s1-20.3.171
- [6] Ernst Trost, Primzahlen, Verlag Birkhäuser, Basel-Stuttgart, 1953 (German). MR 0058630
- [7] Atle Selberg, An elementary proof of the prime-number theorem, Ann. of Math. (2) 50 (1949), 305–313. MR 29410, https://doi.org/10.2307/1969455
- [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. 35 (1949), 374–384. MR 29411, https://doi.org/10.1073/pnas.35.7.374
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1958-0104084-5
Article copyright:
© Copyright 1958
American Mathematical Society