A certain quotient of eta-functions found in Ramanujan's lost notebook
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
Berndt, Bruce C., Heng Huat Chan, Soon-Yi Kang, and Liang-Cheng Zhang. "A certain quotient of eta-functions found in Ramanujan’s lost notebook." Pacific Journal of Mathematics 202, no. 2 (2002): 267-304.
Pacific Journal of Mathematics