Eisenstein series in Ramanujan's lost notebook

Bruce C. Berndt, Heng Huat Chan, Jaebum Sohn, Seung Hwan Son

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

In his lost notebook, Ramanujan stated without proofs several beautiful identities for the three classical Eisenstein series (in Ramanujan's notation) P(q), Q(q), and R(q). The identities are given in terms of certain quotients of Dedekind eta-functions called Hauptmoduls. These identities were first proved by S. Raghavan and S.S. Rangachari, but their proofs used the theory of modular forms, with which Ramanujan was likely unfamiliar. In this paper we prove all these identities by using classical methods which would have been well known to Ramanujan. In fact, all our proofs use only results from Ramanujan's notebooks.

Original languageEnglish
Pages (from-to)81-114
Number of pages34
JournalRamanujan Journal
Volume4
Issue number1
DOIs
Publication statusPublished - 2000 Jan 1

Fingerprint

Ramanujan's Lost Notebook
Eisenstein Series
Ramanujan
Dedekind eta Function
Modular Forms
Notation
Quotient
Likely

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Berndt, Bruce C. ; Chan, Heng Huat ; Sohn, Jaebum ; Son, Seung Hwan. / Eisenstein series in Ramanujan's lost notebook. In: Ramanujan Journal. 2000 ; Vol. 4, No. 1. pp. 81-114.
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Eisenstein series in Ramanujan's lost notebook. / Berndt, Bruce C.; Chan, Heng Huat; Sohn, Jaebum; Son, Seung Hwan.

In: Ramanujan Journal, Vol. 4, No. 1, 01.01.2000, p. 81-114.

Research output: Contribution to journalArticle

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