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

Bruce C. Berndt, Heng Huat Chan, Soon Yi Kang, Liang Cheng Zhang

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)267-304
Number of pages38
JournalPacific Journal of Mathematics
Volume202
Issue number2
DOIs
StatePublished - 2002

ASJC Scopus subject areas

  • Mathematics(all)

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