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XVIII.—The Elementary Proof of the Prime Number Theorem*

Published online by Cambridge University Press:  14 February 2012

E. M. Wright
E. M. Wright
Affiliation:
University of Aberdeen
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Synopsis

The author presents a modification of the recently discovered “elementary” proof of the Prime Number Theorem. Nothing is assumed from the theory of numbers except the Fundamental Theorem of Arithmetic. In the second part of the proof the elements of the integral calculus are used to make clearer the basic ideas on which this part depends.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 63 , Issue 3 , 1952 , pp. 257 - 267
Copyright
Copyright © Royal Society of Edinburgh 1952

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References

REFERENCES TO LITERATURE

Erdös, P., 1949. “On a New Method in Elementary Number Theory which Leads to an Elementary Proof of the Prime Number Theorem”, Proc. Nat. Acad. Sci., xxxv, 374–384.CrossRefGoogle Scholar
Hadamard, J., 1896. “Sur la distribution des zéros de la fonction ζ(s) et ses conséquences arithmétiques”, Bull. Soc. Math. France, xxiv, 199–220.CrossRefGoogle Scholar
Selberg, A., 1949. “An Elementary Proof of the Prime-number Theorem”, Annals of Math., L, 305–313.CrossRefGoogle Scholar
de la Vallèe Poussin, Ch., 1896. “Recherches analytiques sur la théorie des nombres premiers”, Ann. Soc. Sc. Bruxelles, xxi B, 183–256.Google Scholar
Van der Corput, J. G., 1949. “Démonstration élémentaire du théorème sur la distribution des nombres premiers”, Scriptum 1 (Mathematisch Centrum, Amsterdam), 1–32.Google Scholar