Ramanujan partition identity

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1: 26.10 Integer Partitions: Other Restrictions

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§26.10(iv) Identities

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2: 27.14 Unrestricted Partitions

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§27.14(v) Divisibility Properties

►Ramanujan (1921) gives identities that imply divisibility properties of the partition function. For example, the Ramanujan identity …Ramanujan also found that $p\left(7n+5\right)\equiv 0(mod7)$ and $p\left(11n+6\right)\equiv 0(mod11)$ for all $n$. …

3: Bibliography L

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Ramanujan’s function $\tau (n)$ . Duke Math. J. 10 (3), pp. 483–492.

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External Links:

Document, MathReview (H. S. Zuckerman), ZentralBlatt

Referenced by:

§27.20, §27.20, §27.21.

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The vanishing of Ramanujan’s function $\tau (n)$ . Duke Math. J. 14 (2), pp. 429–433.

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External Links:

Document, MathReview (R. A. Rankin), ZentralBlatt

Referenced by:

§27.14(vi).

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A partition function connected with the modulus five. Duke Math. J. 8 (4), pp. 631–655.

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External Links:

Document, MathReview (R. D. James), ZentralBlatt

Referenced by:

§17.18.

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Lie algebraic approaches to classical partition identities. Adv. in Math. 29 (1), pp. 15–59.

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ISSN 0001-8708, Document, MathReview (S. I. Gel’fand), ZentralBlatt

Referenced by:

§17.16.

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A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities. Adv. in Math. 45 (1), pp. 21–72.

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External Links:

ISSN 0001-8708, Document, MathReview (George E. Andrews), ZentralBlatt

Referenced by:

§17.16.

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4: Bibliography

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Chapter $16$ of Ramanujan’s second notebook: Theta-functions and $q$-series. Mem. Amer. Math. Soc. 53 (315), pp. v+85.

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External Links:

ISSN 0065-9266, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§20.11(ii).

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Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, $\pi$, and the Ladies Diary. Amer. Math. Monthly 95 (7), pp. 585–608.

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External Links:

ISSN 0002-9890, FullText, Document, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§19.9(i).

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Ramanujan Revisited. Academic Press Inc., Boston, MA.

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External Links:

ISBN 0-12-058560-X, ISBN 0-12-058560-X, MathReview, ZentralBlatt

Referenced by:

§20.11(ii), Profile Richard A. Askey.

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Plane partitions. III. The weak Macdonald conjecture. Invent. Math. 53 (3), pp. 193–225.

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External Links:

ISSN 0020-9910, Document, MathReview (Edward A. Bender), ZentralBlatt

Referenced by:

§26.12(i), §26.12(ii).

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Multiple series Rogers-Ramanujan type identities. Pacific J. Math. 114 (2), pp. 267–283.

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External Links:

ISSN 0030-8730, MathReview (David M. Bressoud), ZentralBlatt

Referenced by:

§17.12.

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