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Zbl 0061.07905
Erd\H{o}s, Pál
On an elementary proof of some asymptotic formulas in the theory of partitions. (English)
[J] Ann. Math. (2) 43, 437-450 (1942). ISSN 0003-486X; ISSN 1939-0980/e

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 $\lim_{n \to \infty} n p(n) \exp\{-\pi(2n/3)^{1/2}\}$ exists and is positive, but does not determine its value (known to be $48^{-1/2}$). An elementary determination of the value of the limit was later given by {\it D.J.Newman} (Zbl 0043.04501).

Display scanned Zentralblatt-MATH page with this review.
[P.T.Bateman]

MSC 2000:: *11P82 Analytic theory of partitions
11P81 Elementary theory of partitions

Keywords: number theory

Citations: Zbl 0043.04501

Cited in: Zbl 1138.11342 Zbl 1112.11049 Zbl 1016.11048 Zbl 0401.10057

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