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**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 p_{k}(n) be the number of partitions of n into exactly k summands. The author gives an elementary proof that **lim**_{n ––> 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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