Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/103195
Title: Eisenstein series in Ramanujan's lost notebook
Authors: Berndt, B.C.
Chan, H.H. 
Sohn, J.
Son, S.H.
Keywords: Dedekind eta function
Differential equations for Eisenstein series
Eisenstein series
Modular equations
Ramanujan's lost notebook
Theta functions
Issue Date: Mar-2000
Citation: Berndt, B.C.,Chan, H.H.,Sohn, J.,Son, S.H. (2000-03). Eisenstein series in Ramanujan's lost notebook. Ramanujan Journal 4 (1) : 81-114. ScholarBank@NUS Repository.
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.
Source Title: Ramanujan Journal
URI: http://scholarbank.nus.edu.sg/handle/10635/103195
ISSN: 13824090
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

Page view(s)

29
checked on Oct 19, 2018

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.