The Ramanujan Journal

, Volume 19, Issue 2, pp 163–181 | Cite as

Quintic and septic Eisenstein series

Article

Abstract

Using results that were well-known to Ramanujan, we give proofs of some results for Eisenstein series in the lost notebook. Our proofs have the additional advantage that it is not necessary to know the results in advance; that is, the proofs are derivations as opposed to verifications.

Keywords

Convolution sum Dedekind eta function Eisenstein series Lost notebook Modular function Rogers-Ramanujan continued fraction 

Mathematics Subject Classification (2000)

11F20 33E05 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Institute of Information and Mathematical SciencesMassey University-AlbanyAucklandNew Zealand
  2. 2.Department of MathematicsNational University of SingaporeSingaporeSingapore

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