Partition-Theoretic Interpretations of Some q-Series Identities of Ramanujan

Authors

  • Nipen Saikia Rajiv Gandhi University

DOI:

https://doi.org/10.48129/kjs.v48i2.9907

Keywords:

Ramanujan's q-series identities, partition of integer, congruence.

Abstract

Ramanujan's lost notebook contains several $q$-series identities  and some of them have theta-function representations. We give partition-theoretic interpretations of some of these identities  and prove Ramanujan-type congruences for certain partition functions.

Author Biography

Nipen Saikia, Rajiv Gandhi University

Department of Mathematics

Assistant Professor

References

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Springer, New York.

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Berndt, B. C. and Rankin, R. A. (1995).

Ramanujan: Letters and Commentary.

American Mathematical Society.

Hirschhorn, M. D. and and Sellers J. A. (2005).

Arithmetic relations for overpartitions.

Journal of Combinatorial Mathematics

and Combinatorial Computing, 53, 65-

Ramanujan, S.(1919). Some properties of

p(n), the number of partition of n. Proceedings

of the Cambridge Philosophical

Society, 19, 207-210

Ramanujan, S. (1998). The Lost Notebook and

Other Unpublished Papers, Narosa, New

Delhi.

Published

05-04-2021