The Ramanujan Journal

, Volume 18, Issue 1, pp 33–59 | Cite as

Sixteen Eisenstein series

Article

Abstract

S. Ramanujan gave fourteen families of series in his Second Notebook in Chap. 17, Entries 13–17. In each case he gave only the first few examples, giving us the motivation to find and prove a general formula for each family of series. The aim of this paper is to develop a powerful tool (four versatile functions f0,f1,f2, and f3) to collect all of Ramanujan’s examples together.

Keywords

Eisenstein series Elliptic function Ramanujan’s Notebooks Theta function 

Mathematics Subject Classification (2000)

11E25 33D15 33E05 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Institute of Information and Mathematical ScienceMassey UniversityAucklandNew Zealand

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