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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 061.07906

**Autor: ** Erdös, Paul

**Title: ** On some asymptotic formulas in the theory of partitions. (In English)

**Source: ** Bull. Am. Math. Soc. 52, 185-188 (1946).

**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 proves that k_{0}(n) = \pi^{-1}(3/2)^{ ½}n^{ ½} log n+cn^{ ½}+o(n^{ ½}), where c is a constant and k_{0}(n) is the value of k for which p_{k}(n) is largest. Sharper results on k_{0}(n) were subsequently obtained by *G.Szekeres* (Zbl 042.04102).

**Reviewer: ** P.T.Bateman

**Classif.: ** * 11P81 Elementary theory of partitions

11P82 Analytic theory of partitions

**Index Words: ** number theory

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