Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  014.01104
Autor:  Erdös, Pál
Title:  A generalization of a theorem of Besicovitch. (In English)
Source:  J. London Math. Soc. 11, 92-98 (1936).
Review:  Let \deltaa denote the density of the set consisting of all numbers which have a divisor between a and 2a. It was proved by A.S.Besicovitch (see Zbl 009.39504) that liminfa ––> oo \deltaa = 0. Let da denote the density of the set consisting of all numbers which have a divisor between a and a1+\epsilona. The author proves that if \epsilon ––> 0 as a ––> oo then da ––> 0. This is easily seen to be the best possible result of its kind. It is impossible to given a sketch of the highly ingenious proof within the limits of a review.
Reviewer:  Davenport (Cambridge)
Classif.:  * 11N25 Distribution of integers with specified multiplicative constraints
Index Words:  Number theory

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