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Partitions with a restriction on the multiplicity of the summands. (English) Zbl 0213.33402


MSC:

11P82 Analytic theory of partitions
11N37 Asymptotic results on arithmetic functions
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References:

[1] J. W. L. Glaisher, A theorem in partitions, Messenger Math. 12 (1883), 158-170.
[2] Peter Hagis Jr., A problem on partitions with a prime modulus \?\ge 3, Trans. Amer. Math. Soc. 102 (1962), 30 – 62. · Zbl 0101.03402
[3] Peter Hagis Jr., Partitions into odd summands, Amer. J. Math. 85 (1963), 213 – 222. · Zbl 0116.27002
[4] Peter Hagis Jr., A root of unity occurring in partition theory, Proc. Amer. Math. Soc. 26 (1970), 579 – 582. · Zbl 0208.31301
[5] G. H. Hardy and S. Ramanujan, Asymptotic formulae in combinatorial analysis, Proc. London Math. Soc. (2) 17 (1918), 75-115. · JFM 46.0198.04
[6] Loo-keng Hua, On the number of partitions of a number into unequal parts, Trans. Amer. Math. Soc. 51 (1942), 194 – 201. · Zbl 0028.01004
[7] Shô Iseki, A partition function with some congruence condition, Amer. J. Math. 81 (1959), 939 – 961. · Zbl 0094.25605
[8] Joseph Lehner, A partition function connected with the modulus five, Duke Math. J. 8 (1941), 631 – 655. · Zbl 0060.10102
[9] Ivan Niven and Herbert S. Zuckerman, An introduction to the theory of numbers, Second edition, John Wiley & Sons, Inc., New York-London-Sydney, 1966. · Zbl 0154.04002
[10] H. Rademacher, Zur Theorie der Modulfunktionen, J. Reine Angew. Math. 167 (1931), 312-336. · JFM 58.0396.01
[11] Hans Rademacher, The Fourier Coefficients of the Modular Invariant J(\?), Amer. J. Math. 60 (1938), no. 2, 501 – 512. · Zbl 0018.24601
[12] Hans Salié, Zur Abschätzung der Fourierkoeffizienten ganzer Modulformen, Math. Z. 36 (1933), no. 1, 263 – 278 (German). · Zbl 0005.16203
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