Title

A certain quotient of eta-functions found in Ramanujan's lost notebook

Abstract

In his lost notebook, Ramanujan defined a parameter λ 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 λ . 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. n n

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.2140/pjm.2002.202.267

Publication Date

1-1-2002

Journal Title

Pacific Journal of Mathematics

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