Freĭman, G. A. Zur Frage der Zerlegung von Zahlen in eine unbeschränkte Anzahl von Summanden. (Russian) Zbl 0057.03803 Usp. Mat. Nauk 9, No. 3(61), 222-225 (1954). The author states two Tauberian theorems for partitions. One is of the strong type considered by A. E. Ingham [Ann. Math. (2) 42, 1075–1090 (1941; Zbl 0063.02973)], F. C. Auluck and C. B. Haselgrove [Proc. Camb. Philos. Soc. 48, 566–570 (1952; Zbl 0047.28002)], C. B. Haselgrove and H. N. V. Temperley [Proc. Camb. Philos. Soc. 50, 225–241 (1954; Zbl 0055.27401)], and G. Meinardus [Math. Z. 59, 388–398 (1954; Zbl 0055.03806)]. The other is identical with a weaker but more comprehensive result of K. Knopp [Schrift. Königsberg. gelehrt. Ges., naturwiss. Kl. 2, 45–74 (1925; JFM 51.0146.01)], which was subsequently proved again by N. A. Brigham in a more general form [Proc. Am. Math. Soc. 1, 182–191 (1950; Zbl 0037.16903)]. The author remarks that the converse of Knopp’s theorem is also true; in fact, this was proved by P. Erdős [Ann. Math. (2) 43, 437–450 (1942; Zbl 0061.07905)]. Reviewer: P. T. Bateman Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 Review MSC: 11P82 Analytic theory of partitions 40E05 Tauberian theorems Keywords:Tauberian theorems for partitions Citations:Zbl 0063.02973; Zbl 0047.28002; Zbl 0055.27401; JFM 51.0146.01; Zbl 0061.07905; Zbl 0055.03806; Zbl 0037.16903 PDFBibTeX XMLCite \textit{G. A. Freĭman}, Usp. Mat. Nauk 9, No. 3(61), 222--225 (1954; Zbl 0057.03803)