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Some theorems concerning partitions. (English) Zbl 0083.04005


MSC:

11P82 Analytic theory of partitions
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[1] G. H. Hardy, On the representation of a number as the sum of any number of squares, and in particular of five, Trans. Amer. Math. Soc. 21 (1920), no. 3, 255 – 284. · JFM 47.0883.03
[2] G. H. Hardy and S. Ramanujan, Asymptotic formulae in combinatorial analysis, Proc. London Math. Soc. (2) vol. 17 (1918) pp. 75-115. · JFM 46.0198.04
[3] W. K. Hayman, A generalisation of Stirling’s formula, J. Reine Angew. Math. 196 (1956), 67 – 95. · Zbl 0072.06901
[4] E. Hecke, Vorlesungen uber die Theorie der algebr. Zahlen, Leipzig, Akademische Verlagsgeselschaft, 1923. · JFM 49.0106.10
[5] Joseph Lehner, A partition function connected with the modulus five, Duke Math. J. 8 (1941), 631 – 655. · Zbl 0060.10102
[6] John Livingood, A partition function with the prime modulus \?>3, Amer. J. Math. 67 (1945), 194 – 208. · Zbl 0060.10103
[7] Günter Meinardus, Asymptotische Aussagen über Partitionen, Math. Z. 59 (1954), 388 – 398 (German). · Zbl 0055.03806
[8] Hans Petersson, Über Modulfunktionen und Partitionenprobleme, Abh. Deutsch. Akad. Wiss. Berlin. Kl. Math. Allg. Nat. 1954 (1954), no. 2, 59 (German). · Zbl 0057.06801
[9] Hans Petersson, Über die arithmetischen Eigenschaften eines Systems multiplikativer Modulfunktionen von Primzahlstufe, Acta Math. 95 (1956), 57 – 110 (German). · Zbl 0071.04101
[10] H. Rademacher, On the Partitionfunction \( p(n)\), Proc. London Math. Soc. (2) vol. 43 (1937) pp. 241-254. · Zbl 0017.05503
[11] Hans Rademacher, The Fourier Coefficients of the Modular Invariant J(\?), Amer. J. Math. 60 (1938), no. 2, 501 – 512. · Zbl 0018.24601
[12] H. J. Smith, Collected Math. Papers, Clarendon Press, Oxford, 1894.
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