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Transactions of the American Mathematical Society

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On the remainders and convergence of the series for the partition function


Author: D. H. Lehmer
Journal: Trans. Amer. Math. Soc. 46 (1939), 362-373
MSC: Primary 10.0X
Erratum: Trans. Amer. Math. Soc. 259 (1980), 318-318.
MathSciNet review: 0000410
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References [Enhancements On Off] (What's this?)

  • [1] G. H. Hardy and S. Ramanujan, Asymptotic formulæ in combinatory analysis [Proc. London Math. Soc. (2) 17 (1918), 75–115], Collected papers of Srinivasa Ramanujan, AMS Chelsea Publ., Providence, RI, 2000, pp. 276–309. MR 2280879
  • [2] H. Rademacher, On the partition function $ p(n)$, Proceedings of the London Mathematical Society, (2), vol. 43 (1937), pp. 241-254.
  • [3] -, A convergent series for the partition function $ p(n)$, Proceedings of the National Academy of Sciences, vol. 23 (1937), pp. 78-84.
  • [4] D. H. Lehmer, On the series for the partition function, Trans. Amer. Math. Soc. 43 (1938), no. 2, 271–295. MR 1501943, 10.1090/S0002-9947-1938-1501943-5
  • [5] -, An application of the Schläfli's modular equation to a conjecture of Ramanujan, Bulletin of the American Mathematical Society, vol. 44 (1938), pp. 84-90.
  • [6] -, On the Hardy-Ramanujan series for the partition function, Journal of the London Mathematical Society, vol. 12 (1937), pp. 171-176.
  • [7] H. Petersson, Linear relationen zwischen Poincareschen Reihen, Abhandlung des mathematischen Seminars der Hamburgischen Universität, vol. 12 (1938), pp. 415-472.

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DOI: https://doi.org/10.1090/S0002-9947-1939-0000410-9
Article copyright: © Copyright 1939 American Mathematical Society