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Transactions of the American Mathematical Society

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The Ramanujan identities under modular substitutions


Author: Hans Rademacher
Journal: Trans. Amer. Math. Soc. 51 (1942), 609-636
MSC: Primary 10.0X
DOI: https://doi.org/10.1090/S0002-9947-1942-0006204-2
MathSciNet review: 0006204
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  • [1] S. Ramanujan, Some properties of $ p(n)$, the number of partitions of $ n$, Collected Papers, pp. 210-213. MR 2280868
  • [2] L. J. Mordell, Note on certain modular relations considered by Messrs. Ramanujan, Darling, and Rogers, Proceedings of the London Mathematical Society, (2), vol. 20 (1922), pp. 408-416.
  • [3] G. N. Watson, Ramanujans Vermutung über Zerfällungsanzahlen, Journal für die reine und angewandte Mathematik, vol. 179 (1938), pp. 97-128.
  • [4] H. S. Zuckerman, Identities analogous to Ramanujan's identities involving the partition function, Duke Mathematical Journal, vol. 5 (1939), pp. 88-110. MR 1546110
  • [5] F. Klein und R. Fricke, Vorlesungen über die Theorie der Elliptischen Modulfunktionen, vol. 1, 1890, and vol. 2, 1892.
  • [6] R. Fricke, Die Elliptischen Funktionen und ihre Anwendungen, vol. 1, 1916, and vol. 2, 1922.
  • [7] H. Rademacher, Über die Erzeugenden von Kongruenzuntergruppen der Modulgruppe, Abhandlungen aus dem Mathematischen Seminar der Hamburgischen Universität, vol. 7 (1930), pp. 134-148.
  • [8] -, Zur Theorie der Modulfunktionen, Journal für die reine und angewandte Mathematik, vol. 167 (1931), pp. 312-336.
  • [9] H. Rademacher and A. Whiteman, On Dedekind sums, American Journal of Mathematics, vol. 63 (1941), pp. 377-407. MR 0003650 (2:249f)

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DOI: https://doi.org/10.1090/S0002-9947-1942-0006204-2
Article copyright: © Copyright 1942 American Mathematical Society

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