Abstract
Inspired by problem 30.5: “One Old Erdős Problem”
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Erdős, P. (1949). 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 of the United States of America, 35, 374–384.
Erdős, P., & Turán, P. (1934). On a problem in the elementary theory of numbers. American Mathematical Monthly, 41, 608–611.
Hadamard, J. (1893). Etude sur les propriétés des fonctions entiéres et en particulier d’une fonction considérée par Riemann. Journal de Mathématiques Pures et Appliquées, 9(4), 171–215. (reprinted in Oeuvres de Jacques Hadamard, C.N.R.S., Paris, 1968, Vol. 1, 103–147).
Hadamard, J.(1896). Sur la distribution des zéros de la fonction ζ(s) et ses conséquences arithmétiques. Bulletin de la Société Mathématique de France, 24, 199–220. (reprinted in Oeuvres de Jacques Hadamard, C.N.R.S., Paris, 1968, Vol. 1, 189–210).
Selberg, A. (1949). An elementary proof of the prime number theorem. Annals of Mathematics, 50, 305–313.
Spencer, J. H., & Graham, R. L. (2009). The elementary proof of the prime number theorem. The Mathematical Intelligencer, 31(3), 18–23.
de la Vallée Poussin, C. J. (1896). Recherches analytiques sur la théorie des nombres premiers. Annales de la Société scientifique de Bruxelles, 20, 183–256.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Alexander Soifer
About this chapter
Cite this chapter
Soifer, A. (2017). E29: One Old Erdős–Turán Problem. In: The Colorado Mathematical Olympiad: The Third Decade and Further Explorations. Springer, Cham. https://doi.org/10.1007/978-3-319-52861-8_21
Download citation
DOI: https://doi.org/10.1007/978-3-319-52861-8_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-52859-5
Online ISBN: 978-3-319-52861-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)