Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  061.07905
Autor:  Erdös, Pál
Title:  On an elementary proof of some asymptotic formulas in the theory of partitions. (In English)
Source:  Ann. of Math., II. Ser. 43, 437-450 (1942).
Review:  Let p(n) be the number of partitions of the positive integer n and let pk(n) be the number of partitions of n into exactly k summands. The author gives an elementary proof that limn ––> oo n p(n) \exp{-\pi(2n/3) ½} exists and is positive, but does not determine its value (known to be 48- ½). An elementary determination of the value of the limit was later given by D.J.Newman (Zbl 043.04501).
Classif.:  * 11P82 Analytic theory of partitions
                   11P81 Elementary theory of partitions
Index Words:  number theory

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