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Ramanujan partition identity

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1: 26.10 Integer Partitions: Other Restrictions
§26.10(iv) Identities
2: 27.14 Unrestricted Partitions
§27.14(v) Divisibility Properties
Ramanujan (1921) gives identities that imply divisibility properties of the partition function. For example, the Ramanujan identityRamanujan also found that p ( 7 n + 5 ) 0 ( mod 7 ) and p ( 11 n + 6 ) 0 ( mod 11 ) for all n . …
3: Bibliography L
  • D. H. Lehmer (1943) Ramanujan’s function τ ( n ) . Duke Math. J. 10 (3), pp. 483–492.
  • D. H. Lehmer (1947) The vanishing of Ramanujan’s function τ ( n ) . Duke Math. J. 14 (2), pp. 429–433.
  • J. Lehner (1941) A partition function connected with the modulus five. Duke Math. J. 8 (4), pp. 631–655.
  • J. Lepowsky and S. Milne (1978) Lie algebraic approaches to classical partition identities. Adv. in Math. 29 (1), pp. 15–59.
  • J. Lepowsky and R. L. Wilson (1982) A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities. Adv. in Math. 45 (1), pp. 21–72.
  • 4: Bibliography
  • C. Adiga, B. C. Berndt, S. Bhargava, and G. N. Watson (1985) Chapter 16 of Ramanujan’s second notebook: Theta-functions and q -series. Mem. Amer. Math. Soc. 53 (315), pp. v+85.
  • G. Almkvist and B. Berndt (1988) Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, π , and the Ladies Diary. Amer. Math. Monthly 95 (7), pp. 585–608.
  • G. E. Andrews, R. A. Askey, B. C. Berndt, and R. A. Rankin (Eds.) (1988) Ramanujan Revisited. Academic Press Inc., Boston, MA.
  • G. E. Andrews (1979) Plane partitions. III. The weak Macdonald conjecture. Invent. Math. 53 (3), pp. 193–225.
  • G. E. Andrews (1984) Multiple series Rogers-Ramanujan type identities. Pacific J. Math. 114 (2), pp. 267–283.