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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Ramanujan identities under modular substitutions


Author: Hans Rademacher
Journal: Trans. Amer. Math. Soc. 51 (1942), 609-636
MSC: Primary 10.0X
MathSciNet review: 0006204
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  • [1] S. Ramanujan, Some properties of 𝑝(𝑛), the number of partitions of 𝑛 [Proc. Cambridge Philos. Soc. 19 (1919), 207–210], Collected papers of Srinivasa Ramanujan, AMS Chelsea Publ., Providence, RI, 2000, 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] Herbert S. Zuckerman, Identities analogous to Ramanujan’s identities involving the partition function, Duke Math. J. 5 (1939), no. 1, 88–110. MR 1546110, http://dx.doi.org/10.1215/S0012-7094-39-00511-9
  • [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] Hans Rademacher and Albert Whiteman, Theorems on Dedekind sums, Amer. J. Math. 63 (1941), 377–407. MR 0003650 (2,249f)

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DOI: http://dx.doi.org/10.1090/S0002-9947-1942-0006204-2
PII: S 0002-9947(1942)0006204-2
Article copyright: © Copyright 1942 American Mathematical Society