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A SHORT PROOF OF AN IDENTITY FOR CUBIC PARTITION FUNCTION

  • Xiong, Xinhua (Department of Mathematics China Three Gorges University)
  • Received : 2010.06.09
  • Published : 2011.10.31
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Abstract

In this note, we will give a short proof of an identity for cubic partition function.

Keywords

References

  1. H.-C. Chan, Ramanujan's cubic continued fraction and an analog of his \most beautiful identity", Int. J. Number Theory 6 (2010), no. 3, 673-680. https://doi.org/10.1142/S1793042110003150
  2. H.-C. Chan, Ramanujan's cubic continued fraction and Ramanujan type congruences for a ceratin partition function, Int. J. Number Theory, 6 (2010), no. 4, 819-834. https://doi.org/10.1142/S1793042110003241
  3. H.-C. Chan, A new proof of two identities involving Ramanujan's cubic continued fraction, Ramanujan J. 21 (2010), no. 2, 173-180. https://doi.org/10.1007/s11139-009-9203-z
  4. B. Gordon and K. Hughies, Ramanujan congruence for q(n), Analytic number theory (Philadelphia, Pa., 1980), pp. 333-359, Lecture Notes in Math., 899, Springer, Berlin-New York, 1981. https://doi.org/10.1007/BFb0096473
  5. B. Kim, A crank analog on a certain kind of partition function arising from the cubic continued fraction, preprint, 2008.
  6. G. Ligozat, Courbes modulaires de genre 1, Memoires de la Societe Mathematique de France 43 (1975), 5-80.
  7. M. Newman, Constructions and applications of a class of modular functions II, Proc. London Math. Soc. (3) 9 (1959), 373-381. https://doi.org/10.1112/plms/s3-9.3.373
  8. G. N.Watson, Beweis von Ramanujans Vermutungen uber Zerfallungsanzahlen, J. Reine und Angew. Math. 179 (1938), 97-128.
  9. X. H. Xiong, Cubic partition modulo powers of 5, arXiv:math.NT/1004.4737.

Cited by

  1. On the Density of the Odd Values of the Partition Function vol.22, pp.3, 2018, https://doi.org/10.1007/s00026-018-0397-x