Partition-theoretic interpretations of some q-series identities of Ramanujan
DOI:
https://doi.org/10.48129/kjs.v48i2.9907Keywords:
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.References
Andrews, G. E. and Berndt, B.C. (2009).
Ramanujan’s Lost Notebook Part II,
Springer, New York.
Berndt, B. C. (1991). Ramanujan’s Notebooks,
Part III, Springer, New York.
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.
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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Other Unpublished Papers, Narosa, New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.
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Published
05-04-2021
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Section
Mathematics
