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On an elementary proof of some asymptotic formulas in the theory of partitions. (English) Zbl 0061.07905
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 np(n)exp{-π(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 D.J.Newman (Zbl 0043.04501).
Reviewer: P.T.Bateman

MSC:
11P82Analytic theory of partitions
11P81Elementary theory of partitions
Keywords:
number theory