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 pk(n) be the number of partitions of n into exactly k summands. The author proves that

k0(n) = \pi-1(3/2) ½n ½ log n+cn ½+o(n ½),

where c is a constant and k0(n) is the value of k for which pk(n) is largest. Sharper results on k0(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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