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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The Ramanujan identities under modular substitutions
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by Hans Rademacher PDF
Trans. Amer. Math. Soc. 51 (1942), 609-636 Request permission
References
  • 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, DOI 10.1016/s0164-1212(00)00033-9
  • 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. G. N. Watson, Ramanujans Vermutung über Zerfällungsanzahlen, Journal für die reine und angewandte Mathematik, vol. 179 (1938), pp. 97-128.
  • Herbert S. Zuckerman, Identities analogous to Ramanujan’s identities involving the partition function, Duke Math. J. 5 (1939), no. 1, 88–110. MR 1546110, DOI 10.1215/S0012-7094-39-00511-9
  • F. Klein und R. Fricke, Vorlesungen über die Theorie der Elliptischen Modulfunktionen, vol. 1, 1890, and vol. 2, 1892. R. Fricke, Die Elliptischen Funktionen und ihre Anwendungen, vol. 1, 1916, and vol. 2, 1922. H. Rademacher, Über die Erzeugenden von Kongruenzuntergruppen der Modulgruppe, Abhandlungen aus dem Mathematischen Seminar der Hamburgischen Universität, vol. 7 (1930), pp. 134-148. —, Zur Theorie der Modulfunktionen, Journal für die reine und angewandte Mathematik, vol. 167 (1931), pp. 312-336.
  • Hans Rademacher and Albert Whiteman, Theorems on Dedekind sums, Amer. J. Math. 63 (1941), 377–407. MR 3650, DOI 10.2307/2371532
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Additional Information
  • © Copyright 1942 American Mathematical Society
  • 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