The title of this article notwithstanding, it is the author's aspiration here to provide a bit more than merely a glimpse of some of Erdos's contributions per se to probability-statistics. He hopes to have succeeded in providing a guided tour of, and whenever it has appeared feasible, an introduction to, a few selected areas that have been strongly influenced by the work of Erdos. The author also hopes to have succeeded in facilitating a glimpse of the impact of these contributions by presenting them in their historical context.



Nonobstant le titre de son article, l'auteur desire ici fournir davantage qu'un survol des resultats probabilistes et statistiques attribuables specifiquement a Erdos. D espere avoir reussi a donner un tour d'ho-rizon et, la ou faire se peut, une introduction a certains des domaines qui ont ete fortement influences par les travaux d'Erdos. L'auteur souhaite en outre avoir facilite l'appreciation de l'impact de ces differentes contributions en les replacant dans leur contexte historique.

A glimpse of the impact of pál erd#ous on probability and statistics

Erdős and the Integers

There are many ways to recall Paul Erdős’ memory and his special way of doing mathematics. Ernst Straus described him as “the prince of problem solvers and the absolute monarch of problem posers”. Indeed, those mathematicians who are old enough to have attended some of his lectures will remember that, after his talks, chairmen used to slightly depart from standard conduct, not asking if there were any questions but if there were any answers.

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Some of Erdős’ Unconventional Problems in Number Theory, Thirty-four Years Later

Soit { p k ( n )} w ( n ) k =1 la suite croissante des facteurs premiers distincts d'un entier n . Nous donnons, lorsque k → ∞, une approximation uniforme de la loi de repartition limite de la fonction arithmetique n [map ] p k ( n ), precisant ainsi un resultat classique d'Erdős. Deux applications en sont deduites, relatives a la mediane de cette loi et a celle de la fonction “ nombre de facteurs premiers ”.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0305004102005972

P. Erdős

Papers

On the distribution of prime divisors