THE RAMANUJAN JOURNAL, Vol. ?, No. ? (?), ?-?.

Quintic and septic Eisenstein series

SHAUN COOPER
Institute of Information and Mathematical Sciences, Massey University-Albany, Private Bag 102904, North Shore Mail Centre, Auckland,
Email: s.cooper@massey.ac.nz

PEE CHOON TOH
Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Singapore
Email: mattpc@nus.edu.sg

Received August 8, 2007; Accepted January 29, 2008

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:

2000 Mathematics Classification: Primary 11F20; Secondary 33E05