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|Title:||A certain quotient of eta-functions found in Ramanujan's lost notebook||Authors:||Berndt, B.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||URI:||http://scholarbank.nus.edu.sg/handle/10635/102607||ISSN:||00308730|
|Appears in Collections:||Staff Publications|
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