Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.jcta.2004.06.013
Title: Cranks and dissections in Ramanujan's lost notebook
Authors: Berndt, B.C.
Chan, H.H. 
Chan, S.H.
Liaw, W.-C.
Keywords: Congruences for p(n)
Cranks
Dissections
Partition function p(n)
Ramanujan's lost notebook
Issue Date: Jan-2005
Citation: Berndt, B.C., Chan, H.H., Chan, S.H., Liaw, W.-C. (2005-01). Cranks and dissections in Ramanujan's lost notebook. Journal of Combinatorial Theory. Series A 109 (1) : 91-120. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jcta.2004.06.013
Abstract: In his lost notebook, Ramanujan offers several results related to the crank, the existence of which was first conjectured by F. J. Dyson and later established by G.E. Andrews and F.G. Garvan. Using an obscure identity found on p. 59 of the lost notebook, we provide uniform proofs of several congruences in the ring of formal power series for the generating function F (q) of cranks. All are found, sometimes in abbreviated form, in the lost notebook, and imply dissections of F (q). Consequences of our work are interesting new q-series identities and congruences in the spirit of Atkin and Swinnerton-Dyer. © 2004 Elsevier Inc. All rights reserved.
Source Title: Journal of Combinatorial Theory. Series A
URI: http://scholarbank.nus.edu.sg/handle/10635/103083
ISSN: 00973165
DOI: 10.1016/j.jcta.2004.06.013
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