Identities and congruences for the general partition and Ramanujan’s tau functions

Nayandeep Deka Baruah () and Bipul Kumar Sarmah ()
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Nayandeep Deka Baruah: Tezpur University
Bipul Kumar Sarmah: Tezpur University

Indian Journal of Pure and Applied Mathematics, 2013, vol. 44, issue 5, 643-671

Abstract: Abstract We present some identities and congruences for the general partition function p r (n). In particular, we deduce some known identities for Ramanujan’s tau function and find simple proofs of Ramanujan’s famous partition congruences for modulo 5 and 7. Our emphasis throughout this paper is to exhibit the use of Ramanujan’s theta functions to generate identities and congruences for general partition function.

Keywords: Partition; partition congruences; Rogers-Ramanujan continued fraction; Ramanujan’s theta function (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s13226-013-0034-7

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