Zentralblatt MATH

Publications of (and about) Paul Erdös
Zbl.No:  217.32202
Autor:  Erdös, Paul; Turán, P.
Title:  One some general problems in the theory of partitions. I (In English)
Source:  Acta Arith. 18, 53-62 (1971).
Review:  Let 0 < \lambda1 < \lambda2 < ... be an infinite sequence. Assume

limx ––> oo (sum\lambdai < x1 ) X- \alpha(log x)\beta = A.

Then for almost all systems \lambdai1+\lambdai2+... \leq N, 1 \leq i1 < i2 < ... the number of summands is

(1+o(1))c1N\alpha/(\alpha+1)(log N)- \beta /(\alpha+1),   c1 = c1(\alpha,\beta,A).

Several related results are proved. [See the first author and J. Lehner, Duke Math J. 8, 335-345 (1941; Zbl 025.10703) and the authors, Acta Math. Acad. Sci. Hung. 19, 413-435 (1963; Zbl 235.20004).]
Classif.:  * 11P81 Elementary theory of partitions
                   11P82 Analytic theory of partitions

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