Abstract
During the summer of 1975, I spent a few days with my mother and sister who were on holidays near La Baule. I had just left École Polytechnique, and needed some rest after the military service.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
Balasubramanian, Deshouillers and Dress established in 1986 that g(4) = 19, thereby closing up (in a certain sense, which would take us too far to describe here) Waring’s classical problem.
- 2.
See our book Divisors for an expository text on this subject.
- 3.
But this density is strictly positive, which shows that the tendency on which Erdős based his conjecture is nevertheless quite constraining.
References
R. Balasubramanian, J.-M. Deshouillers & F. Dress, Problème de Waring pour les bicarrés, 1 : schéma de la solution, C.R. Acad. Sci. Paris 303 (1986), 85–89.
R. Balasubramanian, J.-M. Deshouillers & F. Dress, Problème de Waring pour les bicarrés, 2 : résultats auxilaires pour le théorème asymptotique, C.R. Acad. Sci. Paris 303 (1986), 161–163.
P. Erdős, On an asymptotic inequality in the theory of numbers (Russian), Vestnik Leningrad Univ. 13 (1960), 41–49.
P. Erdős & G. Tenenbaum, Sur la structure de la suite des diviseurs d’un entier, Ann. Inst. Fourier 31, 1 (1981), 17–37.
H. Halberstam & H.E. Richert, On a result of R.R. Hall, J. Number Theory (1) 11 (1979), 76–89.
H. Halberstam & K.F. Roth, Sequences, Oxford University Press (1966).
R.R. Hall & G. Tenenbaum, Divisors, Cambridge University Press (1988).
H. Maier & G. Tenenbaum, On the set of divisors of an integer, Inventiones Math. 76 (1984), 121–128.
M. Mendès France & G. Tenenbaum, Systèmes de points, diviseurs, et structure fractale, Bull. Soc. Math. de France, Bull. Soc. Math. de France 121 (1993), 197–225.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Tenenbaum, G. (2013). 1105: First Steps in a Mysterious Quest. In: Graham, R., Nešetřil, J., Butler, S. (eds) The Mathematics of Paul Erdős I. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7258-2_20
Download citation
DOI: https://doi.org/10.1007/978-1-4614-7258-2_20
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-7257-5
Online ISBN: 978-1-4614-7258-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)