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Title: A certain quotient of eta-functions found in Ramanujan's lost notebook
Authors: Berndt, B.C.
Chan, H.H. 
Kang, S.-Y.
Zhang, L.-C.
Issue Date: 2002
Citation: Berndt, B.C.,Chan, H.H.,Kang, S.-Y.,Zhang, L.-C. (2002). A certain quotient of eta-functions found in Ramanujan's lost notebook. Pacific Journal of Mathematics 202 (2) : 267-304. ScholarBank@NUS Repository.
Abstract: In his lost notebook, Ramanujan defined a parameter λn by a certain quotient of Dedekind eta-functions at the argument q = exp(-π√n/3). He then recorded a table of several values of λn. To prove these values (and others), we develop several methods, which include modular equations, the modular j-invariant, Kronecker's limit formula, Ramanujan's "cubic theory" of elliptic functions, and an empirical process.
Source Title: Pacific Journal of Mathematics
ISSN: 00308730
Appears in Collections:Staff Publications

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